Exemple #1
0
  /**
   * Converts the floating point value to its exponent-mantissa representation. The mantissa
   * occupies the 11 least significant bits (bits 10-0), and the exponent the previous 5 bits (bits
   * 15-11).
   *
   * @param step The quantization step, normalized to a dynamic range of 1.
   * @return The exponent mantissa representation of the step.
   */
  public static int convertToExpMantissa(float step) {
    int exp;

    exp = (int) Math.ceil(-Math.log(step) / log2);
    if (exp > QSTEP_MAX_EXPONENT) {
      // If step size is too small for exponent representation, use the
      // minimum, which is exponent QSTEP_MAX_EXPONENT and mantissa 0.
      return (QSTEP_MAX_EXPONENT << QSTEP_MANTISSA_BITS);
    }
    // NOTE: this formula does not support more than 5 bits for the
    // exponent, otherwise (-1<<exp) might overflow (the - is used to be
    // able to represent 2**31)
    return (exp << QSTEP_MANTISSA_BITS)
        | ((int) ((-step * (-1 << exp) - 1f) * (1 << QSTEP_MANTISSA_BITS) + 0.5f));
  }
Exemple #2
0
  /**
   * Returns the maximum number of magnitude bits in any subband in the given tile-component if
   * derived quantization is used
   *
   * @param sb The root of the subband tree of the tile-component
   * @param t Tile index
   * @param c Component index
   * @return The highest number of magnitude bit-planes
   */
  private int getMaxMagBitsDerived(Subband sb, int t, int c) {
    int tmp, max = 0;
    int g = ((Integer) gbs.getTileCompVal(t, c)).intValue();

    if (!sb.isNode) {
      float baseStep = ((Float) qsss.getTileCompVal(t, c)).floatValue();
      return g - 1 + sb.level - (int) Math.floor(Math.log(baseStep) / log2);
    }

    max = getMaxMagBitsDerived(sb.getLL(), t, c);
    tmp = getMaxMagBitsDerived(sb.getLH(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsDerived(sb.getHL(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsDerived(sb.getHH(), t, c);
    if (tmp > max) max = tmp;

    return max;
  }
Exemple #3
0
  /**
   * Returns the maximum number of magnitude bits in any subband in the given tile-component if
   * expounded quantization is used
   *
   * @param sb The root of the subband tree of the tile-component
   * @param t Tile index
   * @param c Component index
   * @return The highest number of magnitude bit-planes
   */
  private int getMaxMagBitsExpounded(Subband sb, int t, int c) {
    int tmp, max = 0;
    int g = ((Integer) gbs.getTileCompVal(t, c)).intValue();

    if (!sb.isNode) {
      float baseStep = ((Float) qsss.getTileCompVal(t, c)).floatValue();
      return g
          - 1
          - (int)
              Math.floor(
                  Math.log(baseStep / (((SubbandAn) sb).l2Norm * (1 << sb.anGainExp))) / log2);
    }

    max = getMaxMagBitsExpounded(sb.getLL(), t, c);
    tmp = getMaxMagBitsExpounded(sb.getLH(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsExpounded(sb.getHL(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsExpounded(sb.getHH(), t, c);
    if (tmp > max) max = tmp;

    return max;
  }
Exemple #4
0
  /**
   * Returns the next code-block in the current tile for the specified component. The order in which
   * code-blocks are returned is not specified. However each code-block is returned only once and
   * all code-blocks will be returned if the method is called 'N' times, where 'N' is the number of
   * code-blocks in the tile. After all the code-blocks have been returned for the current tile
   * calls to this method will return 'null'.
   *
   * <p>When changing the current tile (through 'setTile()' or 'nextTile()') this method will always
   * return the first code-block, as if this method was never called before for the new current
   * tile.
   *
   * <p>The data returned by this method can be the data in the internal buffer of this object, if
   * any, and thus can not be modified by the caller. The 'offset' and 'scanw' of the returned data
   * can be arbitrary. See the 'CBlkWTData' class.
   *
   * <p>The 'ulx' and 'uly' members of the returned 'CBlkWTData' object contain the coordinates of
   * the top-left corner of the block, with respect to the tile, not the subband.
   *
   * @param c The component for which to return the next code-block.
   * @param cblk If non-null this object will be used to return the new code-block. If null a new
   *     one will be allocated and returned. If the "data" array of the object is non-null it will
   *     be reused, if possible, to return the data.
   * @return The next code-block in the current tile for component 'n', or null if all code-blocks
   *     for the current tile have been returned.
   * @see CBlkWTData
   */
  public final CBlkWTData getNextInternCodeBlock(int c, CBlkWTData cblk) {
    // NOTE: this method is declared final since getNextCodeBlock() relies
    // on this particular implementation
    int k, j;
    int tmp, shiftBits, jmin;
    int w, h;
    int outarr[];
    float infarr[] = null;
    CBlkWTDataFloat infblk;
    float invstep; // The inverse of the quantization step size
    boolean intq; // flag for quantizig ints
    SubbandAn sb;
    float stepUDR; // The quantization step size (for a dynamic
    // range of 1, or unit)
    int g = ((Integer) gbs.getTileCompVal(tIdx, c)).intValue();

    // Are we quantizing ints or floats?
    intq = (src.getDataType(tIdx, c) == DataBlk.TYPE_INT);

    // Check that we have an output object
    if (cblk == null) {
      cblk = new CBlkWTDataInt();
    }

    // Cache input float code-block
    infblk = this.infblk;

    // Get data to quantize. When quantizing int data 'cblk' is used to
    // get the data to quantize and to return the quantized data as well,
    // that's why 'getNextCodeBlock()' is used. This can not be done when
    // quantizing float data because of the different data types, that's
    // why 'getNextInternCodeBlock()' is used in that case.
    if (intq) { // Source data is int
      cblk = src.getNextCodeBlock(c, cblk);
      if (cblk == null) {
        return null; // No more code-blocks in current tile for comp.
      }
      // Input and output arrays are the same (for "in place" quant.)
      outarr = (int[]) cblk.getData();
    } else { // Source data is float
      // Can not use 'cblk' to get float data, use 'infblk'
      infblk = (CBlkWTDataFloat) src.getNextInternCodeBlock(c, infblk);
      if (infblk == null) {
        // Release buffer from infblk: this enables to garbage collect
        // the big buffer when we are done with last code-block of
        // component.
        this.infblk.setData(null);
        return null; // No more code-blocks in current tile for comp.
      }
      this.infblk = infblk; // Save local cache
      infarr = (float[]) infblk.getData();
      // Get output data array and check that there is memory to put the
      // quantized coeffs in
      outarr = (int[]) cblk.getData();
      if (outarr == null || outarr.length < infblk.w * infblk.h) {
        outarr = new int[infblk.w * infblk.h];
        cblk.setData(outarr);
      }
      cblk.m = infblk.m;
      cblk.n = infblk.n;
      cblk.sb = infblk.sb;
      cblk.ulx = infblk.ulx;
      cblk.uly = infblk.uly;
      cblk.w = infblk.w;
      cblk.h = infblk.h;
      cblk.wmseScaling = infblk.wmseScaling;
      cblk.offset = 0;
      cblk.scanw = cblk.w;
    }

    // Cache width, height and subband of code-block
    w = cblk.w;
    h = cblk.h;
    sb = cblk.sb;

    if (isReversible(tIdx, c)) { // Reversible only for int data
      cblk.magbits = g - 1 + src.getNomRangeBits(c) + sb.anGainExp;
      shiftBits = 31 - cblk.magbits;

      // Update the convertFactor field
      cblk.convertFactor = (1 << shiftBits);

      // Since we used getNextCodeBlock() to get the int data then
      // 'offset' is 0 and 'scanw' is the width of the code-block The
      // input and output arrays are the same (i.e. "in place")
      for (j = w * h - 1; j >= 0; j--) {
        tmp = (outarr[j] << shiftBits);
        outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
      }
    } else { // Non-reversible, use step size
      float baseStep = ((Float) qsss.getTileCompVal(tIdx, c)).floatValue();

      // Calculate magnitude bits and quantization step size
      if (isDerived(tIdx, c)) {
        cblk.magbits = g - 1 + sb.level - (int) Math.floor(Math.log(baseStep) / log2);
        stepUDR = baseStep / (1 << sb.level);
      } else {
        cblk.magbits =
            g - 1 - (int) Math.floor(Math.log(baseStep / (sb.l2Norm * (1 << sb.anGainExp))) / log2);
        stepUDR = baseStep / (sb.l2Norm * (1 << sb.anGainExp));
      }
      shiftBits = 31 - cblk.magbits;
      // Calculate step that decoder will get and use that one.
      stepUDR = convertFromExpMantissa(convertToExpMantissa(stepUDR));
      invstep = 1.0f / ((1L << (src.getNomRangeBits(c) + sb.anGainExp)) * stepUDR);
      // Normalize to magnitude bits (output fractional point)
      invstep *= (1 << (shiftBits - src.getFixedPoint(c)));

      // Update convertFactor and stepSize fields
      cblk.convertFactor = invstep;
      cblk.stepSize = ((1L << (src.getNomRangeBits(c) + sb.anGainExp)) * stepUDR);

      if (intq) { // Quantizing int data
        // Since we used getNextCodeBlock() to get the int data then
        // 'offset' is 0 and 'scanw' is the width of the code-block
        // The input and output arrays are the same (i.e. "in place")
        for (j = w * h - 1; j >= 0; j--) {
          tmp = (int) (outarr[j] * invstep);
          outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
        }
      } else { // Quantizing float data
        for (j = w * h - 1, k = infblk.offset + (h - 1) * infblk.scanw + w - 1, jmin = w * (h - 1);
            j >= 0;
            jmin -= w) {
          for (; j >= jmin; k--, j--) {
            tmp = (int) (infarr[k] * invstep);
            outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
          }
          // Jump to beggining of previous line in input
          k -= infblk.scanw - w;
        }
      }
    }
    // Return the quantized code-block
    return cblk;
  }
Exemple #5
0
/**
 * This class implements scalar quantization of integer or floating-point valued source data. The
 * source data is the wavelet transformed image data and the output is the quantized wavelet
 * coefficients represented in sign-magnitude (see below).
 *
 * <p>Sign magnitude representation is used (instead of two's complement) for the output data. The
 * most significant bit is used for the sign (0 if positive, 1 if negative). Then the magnitude of
 * the quantized coefficient is stored in the next M most significat bits. The rest of the bits
 * (least significant bits) can contain a fractional value of the quantized coefficient. This
 * fractional value is not to be coded by the entropy coder. However, it can be used to compute
 * rate-distortion measures with greater precision.
 *
 * <p>The value of M is determined for each subband as the sum of the number of guard bits G and the
 * nominal range of quantized wavelet coefficients in the corresponding subband (Rq), minus 1:
 *
 * <p>M = G + Rq -1
 *
 * <p>The value of G should be the same for all subbands. The value of Rq depends on the
 * quantization step size, the nominal range of the component before the wavelet transform and the
 * analysis gain of the subband (see Subband).
 *
 * <p>The blocks of data that are requested should not cross subband boundaries.
 *
 * @see Subband
 * @see Quantizer
 */
public class StdQuantizer extends Quantizer {

  /** The number of mantissa bits for the quantization steps */
  public static final int QSTEP_MANTISSA_BITS = 11;

  /** The number of exponent bits for the quantization steps */
  // NOTE: formulas in 'convertFromExpMantissa()' and
  // 'convertToExpMantissa()' methods do not support more than 5 bits.
  public static final int QSTEP_EXPONENT_BITS = 5;

  /** The maximum value of the mantissa for the quantization steps */
  public static final int QSTEP_MAX_MANTISSA = (1 << QSTEP_MANTISSA_BITS) - 1;

  /** The maximum value of the exponent for the quantization steps */
  public static final int QSTEP_MAX_EXPONENT = (1 << QSTEP_EXPONENT_BITS) - 1;

  /** Natural log of 2, used as a convenience variable */
  private static double log2 = Math.log(2);

  /** The quantization type specifications */
  private QuantTypeSpec qts;

  /** The quantization step size specifications */
  private QuantStepSizeSpec qsss;

  /** The guard bits specifications */
  private GuardBitsSpec gbs;

  /**
   * The 'CBlkWTDataFloat' object used to request data, used when quantizing floating-point data.
   */
  // This variable makes the class thread unsafe, but it avoids allocating
  // new objects for code-block that is quantized.
  private CBlkWTDataFloat infblk;

  /**
   * Initializes the source of wavelet transform coefficients. The constructor takes information on
   * whether the quantizer is in reversible, derived or expounded mode. If the quantizer is
   * reversible the value of 'derived' is ignored. If the source data is not integer (int) then the
   * quantizer can not be reversible.
   *
   * <p>After initializing member attributes, getAnSubbandTree is called for all components setting
   * the 'stepWMSE' for all subbands in the current tile.
   *
   * @param src The source of wavelet transform coefficients.
   * @param encSpec The encoder specifications
   */
  public StdQuantizer(CBlkWTDataSrc src, J2KImageWriteParamJava wp) {
    super(src);
    qts = wp.getQuantizationType();
    qsss = wp.getQuantizationStep();
    gbs = wp.getGuardBits();
  }

  /**
   * Returns the quantization type spec object associated to the quantizer.
   *
   * @return The quantization type spec
   */
  public QuantTypeSpec getQuantTypeSpec() {
    return qts;
  }

  /**
   * Returns the number of guard bits used by this quantizer in the given tile-component.
   *
   * @param t Tile index
   * @param c Component index
   * @return The number of guard bits
   */
  public int getNumGuardBits(int t, int c) {
    return ((Integer) gbs.getTileCompVal(t, c)).intValue();
  }

  /**
   * Returns true if the quantized data is reversible, for the specified tile-component. For the
   * quantized data to be reversible it is necessary and sufficient that the quantization is
   * reversible.
   *
   * @param t The tile to test for reversibility
   * @param c The component to test for reversibility
   * @return True if the quantized data is reversible, false if not.
   */
  public boolean isReversible(int t, int c) {
    return qts.isReversible(t, c);
  }

  /**
   * Returns true if given tile-component uses derived quantization step sizes.
   *
   * @param t Tile index
   * @param c Component index
   * @return True if derived
   */
  public boolean isDerived(int t, int c) {
    return qts.isDerived(t, c);
  }

  /**
   * Returns the next code-block in the current tile for the specified component, as a copy (see
   * below). The order in which code-blocks are returned is not specified. However each code-block
   * is returned only once and all code-blocks will be returned if the method is called 'N' times,
   * where 'N' is the number of code-blocks in the tile. After all the code-blocks have been
   * returned for the current tile calls to this method will return 'null'.
   *
   * <p>When changing the current tile (through 'setTile()' or 'nextTile()') this method will always
   * return the first code-block, as if this method was never called before for the new current
   * tile.
   *
   * <p>The data returned by this method is always a copy of the data. Therfore it can be modified
   * "in place" without any problems after being returned. The 'offset' of the returned data is 0,
   * and the 'scanw' is the same as the code-block width. See the 'CBlkWTData' class.
   *
   * <p>The 'ulx' and 'uly' members of the returned 'CBlkWTData' object contain the coordinates of
   * the top-left corner of the block, with respect to the tile, not the subband.
   *
   * @param c The component for which to return the next code-block.
   * @param cblk If non-null this object will be used to return the new code-block. If null a new
   *     one will be allocated and returned. If the "data" array of the object is non-null it will
   *     be reused, if possible, to return the data.
   * @return The next code-block in the current tile for component 'n', or null if all code-blocks
   *     for the current tile have been returned.
   * @see CBlkWTData
   */
  public CBlkWTData getNextCodeBlock(int c, CBlkWTData cblk) {
    return getNextInternCodeBlock(c, cblk);
  }

  /**
   * Returns the next code-block in the current tile for the specified component. The order in which
   * code-blocks are returned is not specified. However each code-block is returned only once and
   * all code-blocks will be returned if the method is called 'N' times, where 'N' is the number of
   * code-blocks in the tile. After all the code-blocks have been returned for the current tile
   * calls to this method will return 'null'.
   *
   * <p>When changing the current tile (through 'setTile()' or 'nextTile()') this method will always
   * return the first code-block, as if this method was never called before for the new current
   * tile.
   *
   * <p>The data returned by this method can be the data in the internal buffer of this object, if
   * any, and thus can not be modified by the caller. The 'offset' and 'scanw' of the returned data
   * can be arbitrary. See the 'CBlkWTData' class.
   *
   * <p>The 'ulx' and 'uly' members of the returned 'CBlkWTData' object contain the coordinates of
   * the top-left corner of the block, with respect to the tile, not the subband.
   *
   * @param c The component for which to return the next code-block.
   * @param cblk If non-null this object will be used to return the new code-block. If null a new
   *     one will be allocated and returned. If the "data" array of the object is non-null it will
   *     be reused, if possible, to return the data.
   * @return The next code-block in the current tile for component 'n', or null if all code-blocks
   *     for the current tile have been returned.
   * @see CBlkWTData
   */
  public final CBlkWTData getNextInternCodeBlock(int c, CBlkWTData cblk) {
    // NOTE: this method is declared final since getNextCodeBlock() relies
    // on this particular implementation
    int k, j;
    int tmp, shiftBits, jmin;
    int w, h;
    int outarr[];
    float infarr[] = null;
    CBlkWTDataFloat infblk;
    float invstep; // The inverse of the quantization step size
    boolean intq; // flag for quantizig ints
    SubbandAn sb;
    float stepUDR; // The quantization step size (for a dynamic
    // range of 1, or unit)
    int g = ((Integer) gbs.getTileCompVal(tIdx, c)).intValue();

    // Are we quantizing ints or floats?
    intq = (src.getDataType(tIdx, c) == DataBlk.TYPE_INT);

    // Check that we have an output object
    if (cblk == null) {
      cblk = new CBlkWTDataInt();
    }

    // Cache input float code-block
    infblk = this.infblk;

    // Get data to quantize. When quantizing int data 'cblk' is used to
    // get the data to quantize and to return the quantized data as well,
    // that's why 'getNextCodeBlock()' is used. This can not be done when
    // quantizing float data because of the different data types, that's
    // why 'getNextInternCodeBlock()' is used in that case.
    if (intq) { // Source data is int
      cblk = src.getNextCodeBlock(c, cblk);
      if (cblk == null) {
        return null; // No more code-blocks in current tile for comp.
      }
      // Input and output arrays are the same (for "in place" quant.)
      outarr = (int[]) cblk.getData();
    } else { // Source data is float
      // Can not use 'cblk' to get float data, use 'infblk'
      infblk = (CBlkWTDataFloat) src.getNextInternCodeBlock(c, infblk);
      if (infblk == null) {
        // Release buffer from infblk: this enables to garbage collect
        // the big buffer when we are done with last code-block of
        // component.
        this.infblk.setData(null);
        return null; // No more code-blocks in current tile for comp.
      }
      this.infblk = infblk; // Save local cache
      infarr = (float[]) infblk.getData();
      // Get output data array and check that there is memory to put the
      // quantized coeffs in
      outarr = (int[]) cblk.getData();
      if (outarr == null || outarr.length < infblk.w * infblk.h) {
        outarr = new int[infblk.w * infblk.h];
        cblk.setData(outarr);
      }
      cblk.m = infblk.m;
      cblk.n = infblk.n;
      cblk.sb = infblk.sb;
      cblk.ulx = infblk.ulx;
      cblk.uly = infblk.uly;
      cblk.w = infblk.w;
      cblk.h = infblk.h;
      cblk.wmseScaling = infblk.wmseScaling;
      cblk.offset = 0;
      cblk.scanw = cblk.w;
    }

    // Cache width, height and subband of code-block
    w = cblk.w;
    h = cblk.h;
    sb = cblk.sb;

    if (isReversible(tIdx, c)) { // Reversible only for int data
      cblk.magbits = g - 1 + src.getNomRangeBits(c) + sb.anGainExp;
      shiftBits = 31 - cblk.magbits;

      // Update the convertFactor field
      cblk.convertFactor = (1 << shiftBits);

      // Since we used getNextCodeBlock() to get the int data then
      // 'offset' is 0 and 'scanw' is the width of the code-block The
      // input and output arrays are the same (i.e. "in place")
      for (j = w * h - 1; j >= 0; j--) {
        tmp = (outarr[j] << shiftBits);
        outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
      }
    } else { // Non-reversible, use step size
      float baseStep = ((Float) qsss.getTileCompVal(tIdx, c)).floatValue();

      // Calculate magnitude bits and quantization step size
      if (isDerived(tIdx, c)) {
        cblk.magbits = g - 1 + sb.level - (int) Math.floor(Math.log(baseStep) / log2);
        stepUDR = baseStep / (1 << sb.level);
      } else {
        cblk.magbits =
            g - 1 - (int) Math.floor(Math.log(baseStep / (sb.l2Norm * (1 << sb.anGainExp))) / log2);
        stepUDR = baseStep / (sb.l2Norm * (1 << sb.anGainExp));
      }
      shiftBits = 31 - cblk.magbits;
      // Calculate step that decoder will get and use that one.
      stepUDR = convertFromExpMantissa(convertToExpMantissa(stepUDR));
      invstep = 1.0f / ((1L << (src.getNomRangeBits(c) + sb.anGainExp)) * stepUDR);
      // Normalize to magnitude bits (output fractional point)
      invstep *= (1 << (shiftBits - src.getFixedPoint(c)));

      // Update convertFactor and stepSize fields
      cblk.convertFactor = invstep;
      cblk.stepSize = ((1L << (src.getNomRangeBits(c) + sb.anGainExp)) * stepUDR);

      if (intq) { // Quantizing int data
        // Since we used getNextCodeBlock() to get the int data then
        // 'offset' is 0 and 'scanw' is the width of the code-block
        // The input and output arrays are the same (i.e. "in place")
        for (j = w * h - 1; j >= 0; j--) {
          tmp = (int) (outarr[j] * invstep);
          outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
        }
      } else { // Quantizing float data
        for (j = w * h - 1, k = infblk.offset + (h - 1) * infblk.scanw + w - 1, jmin = w * (h - 1);
            j >= 0;
            jmin -= w) {
          for (; j >= jmin; k--, j--) {
            tmp = (int) (infarr[k] * invstep);
            outarr[j] = ((tmp < 0) ? (1 << 31) | (-tmp) : tmp);
          }
          // Jump to beggining of previous line in input
          k -= infblk.scanw - w;
        }
      }
    }
    // Return the quantized code-block
    return cblk;
  }

  /**
   * Calculates the parameters of the SubbandAn objects that depend on the Quantizer. The 'stepWMSE'
   * field is calculated for each subband which is a leaf in the tree rooted at 'sb', for the
   * specified component. The subband tree 'sb' must be the one for the component 'n'.
   *
   * @param sb The root of the subband tree.
   * @param c The component index
   * @see SubbandAn#stepWMSE
   */
  protected void calcSbParams(SubbandAn sb, int c) {
    float baseStep;

    if (sb.stepWMSE > 0f) // parameters already calculated
    return;
    if (!sb.isNode) {
      if (isReversible(tIdx, c)) {
        sb.stepWMSE = (float) Math.pow(2, -(src.getNomRangeBits(c) << 1)) * sb.l2Norm * sb.l2Norm;
      } else {
        baseStep = ((Float) qsss.getTileCompVal(tIdx, c)).floatValue();
        if (isDerived(tIdx, c)) {
          sb.stepWMSE =
              baseStep
                  * baseStep
                  * (float) Math.pow(2, (sb.anGainExp - sb.level) << 1)
                  * sb.l2Norm
                  * sb.l2Norm;
        } else {
          sb.stepWMSE = baseStep * baseStep;
        }
      }
    } else {
      calcSbParams((SubbandAn) sb.getLL(), c);
      calcSbParams((SubbandAn) sb.getHL(), c);
      calcSbParams((SubbandAn) sb.getLH(), c);
      calcSbParams((SubbandAn) sb.getHH(), c);
      sb.stepWMSE = 1f; // Signal that we already calculated this branch
    }
  }

  /**
   * Converts the floating point value to its exponent-mantissa representation. The mantissa
   * occupies the 11 least significant bits (bits 10-0), and the exponent the previous 5 bits (bits
   * 15-11).
   *
   * @param step The quantization step, normalized to a dynamic range of 1.
   * @return The exponent mantissa representation of the step.
   */
  public static int convertToExpMantissa(float step) {
    int exp;

    exp = (int) Math.ceil(-Math.log(step) / log2);
    if (exp > QSTEP_MAX_EXPONENT) {
      // If step size is too small for exponent representation, use the
      // minimum, which is exponent QSTEP_MAX_EXPONENT and mantissa 0.
      return (QSTEP_MAX_EXPONENT << QSTEP_MANTISSA_BITS);
    }
    // NOTE: this formula does not support more than 5 bits for the
    // exponent, otherwise (-1<<exp) might overflow (the - is used to be
    // able to represent 2**31)
    return (exp << QSTEP_MANTISSA_BITS)
        | ((int) ((-step * (-1 << exp) - 1f) * (1 << QSTEP_MANTISSA_BITS) + 0.5f));
  }

  /**
   * Converts the exponent-mantissa representation to its floating-point value. The mantissa
   * occupies the 11 least significant bits (bits 10-0), and the exponent the previous 5 bits (bits
   * 15-11).
   *
   * @param ems The exponent-mantissa representation of the step.
   * @return The floating point representation of the step, normalized to a dynamic range of 1.
   */
  private static float convertFromExpMantissa(int ems) {
    // NOTE: this formula does not support more than 5 bits for the
    // exponent, otherwise (-1<<exp) might overflow (the - is used to be
    // able to represent 2**31)
    return (-1f - ((float) (ems & QSTEP_MAX_MANTISSA)) / ((float) (1 << QSTEP_MANTISSA_BITS)))
        / (float) (-1 << ((ems >> QSTEP_MANTISSA_BITS) & QSTEP_MAX_EXPONENT));
  }

  /**
   * Returns the maximum number of magnitude bits in any subband of the current tile.
   *
   * @param c the component number
   * @return The maximum number of magnitude bits in all subbands of the current tile.
   */
  public int getMaxMagBits(int c) {
    Subband sb = getAnSubbandTree(tIdx, c);
    if (isReversible(tIdx, c)) {
      return getMaxMagBitsRev(sb, c);
    } else {
      if (isDerived(tIdx, c)) {
        return getMaxMagBitsDerived(sb, tIdx, c);
      } else {
        return getMaxMagBitsExpounded(sb, tIdx, c);
      }
    }
  }

  /**
   * Returns the maximum number of magnitude bits in any subband of the current tile if reversible
   * quantization is used
   *
   * @param sb The root of the subband tree of the current tile
   * @param c the component number
   * @return The highest number of magnitude bit-planes
   */
  private int getMaxMagBitsRev(Subband sb, int c) {
    int tmp, max = 0;
    int g = ((Integer) gbs.getTileCompVal(tIdx, c)).intValue();

    if (!sb.isNode) return g - 1 + src.getNomRangeBits(c) + sb.anGainExp;

    max = getMaxMagBitsRev(sb.getLL(), c);
    tmp = getMaxMagBitsRev(sb.getLH(), c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsRev(sb.getHL(), c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsRev(sb.getHH(), c);
    if (tmp > max) max = tmp;

    return max;
  }

  /**
   * Returns the maximum number of magnitude bits in any subband in the given tile-component if
   * derived quantization is used
   *
   * @param sb The root of the subband tree of the tile-component
   * @param t Tile index
   * @param c Component index
   * @return The highest number of magnitude bit-planes
   */
  private int getMaxMagBitsDerived(Subband sb, int t, int c) {
    int tmp, max = 0;
    int g = ((Integer) gbs.getTileCompVal(t, c)).intValue();

    if (!sb.isNode) {
      float baseStep = ((Float) qsss.getTileCompVal(t, c)).floatValue();
      return g - 1 + sb.level - (int) Math.floor(Math.log(baseStep) / log2);
    }

    max = getMaxMagBitsDerived(sb.getLL(), t, c);
    tmp = getMaxMagBitsDerived(sb.getLH(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsDerived(sb.getHL(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsDerived(sb.getHH(), t, c);
    if (tmp > max) max = tmp;

    return max;
  }

  /**
   * Returns the maximum number of magnitude bits in any subband in the given tile-component if
   * expounded quantization is used
   *
   * @param sb The root of the subband tree of the tile-component
   * @param t Tile index
   * @param c Component index
   * @return The highest number of magnitude bit-planes
   */
  private int getMaxMagBitsExpounded(Subband sb, int t, int c) {
    int tmp, max = 0;
    int g = ((Integer) gbs.getTileCompVal(t, c)).intValue();

    if (!sb.isNode) {
      float baseStep = ((Float) qsss.getTileCompVal(t, c)).floatValue();
      return g
          - 1
          - (int)
              Math.floor(
                  Math.log(baseStep / (((SubbandAn) sb).l2Norm * (1 << sb.anGainExp))) / log2);
    }

    max = getMaxMagBitsExpounded(sb.getLL(), t, c);
    tmp = getMaxMagBitsExpounded(sb.getLH(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsExpounded(sb.getHL(), t, c);
    if (tmp > max) max = tmp;
    tmp = getMaxMagBitsExpounded(sb.getHH(), t, c);
    if (tmp > max) max = tmp;

    return max;
  }
}