.. index::
   single: Compression mode

|zfp| accepts one or more parameters for specifying how the data is to be compressed to meet various constraints on accuracy or size. At a high level, there are five different compression modes that are mutually exclusive: :ref:`expert <mode-expert>`, :ref:`fixed-rate <mode-fixed-rate>`, :ref:`fixed-precision <mode-fixed-precision>`, :ref:`fixed-accuracy <mode-fixed-accuracy>`, and :ref:`reversible <mode-reversible>` mode. The user has to select one of these modes and its corresponding parameters. In streaming I/O applications, the :ref:`fixed-accuracy mode <mode-fixed-accuracy>` is preferred, as it provides the highest quality (in the absolute error sense) per bit of compressed storage.

The :c:type:`zfp_stream` struct encapsulates the compression parameters and other information about the compressed stream. Its members should not be manipulated directly. Instead, use the access functions (see the :ref:`C API <hl-api>` section) for setting and querying them. One can verify the active compression mode on a :c:type:`zfp_stream` through :c:func:`zfp_stream_compression_mode`. The members that govern the compression parameters are described below.

.. index::
   single: Compression mode; Expert mode

The most general mode is the 'expert mode,' which takes four integer parameters. Although most users will not directly select this mode, we discuss it first since the other modes can be expressed in terms of setting expert mode parameters.

The four parameters denote constraints that are applied to each block in the :ref:`compression algorithm <algorithm-lossy>`. Compression is terminated as soon as one of these constraints is not met, which has the effect of truncating the compressed bit stream that encodes the block. The four constraints are as follows:

.. c:member:: uint zfp_stream.minbits

  The minimum number of compressed bits used to represent a block.  Usually
  this parameter equals one bit, unless each and every block is to be stored
  using a fixed number of bits to facilitate random access, in which case it
  should be set to the same value as :c:member:`zfp_stream.maxbits`.

.. c:member:: uint zfp_stream.maxbits

  The maximum number of bits used to represent a block.  This parameter
  sets a hard upper bound on compressed block size, and governs the rate
  in :ref:`fixed-rate mode <mode-fixed-rate>`.  It may also be used as an
  upper storage limit to guard against buffer overruns in combination with
  the accuracy constraints given by :c:member:`zfp_stream.maxprec` and
  :c:member:`zfp_stream.minexp`.

.. c:member:: uint zfp_stream.maxprec

  The maximum number of bit planes encoded.  This parameter governs the number
  of most significant uncompressed bits encoded per transform coefficient.
  It does not directly correspond to the number of uncompressed mantissa bits
  for the floating-point or integer values being compressed, but is closely
  :ref:`related <q-relerr>`.  This is the parameter that specifies the
  precision in :ref:`fixed-precision mode <mode-fixed-precision>`, and it
  provides a mechanism for controlling the *relative error*.  Note that this
  parameter selects how many bits planes to encode regardless of the magnitude
  of the common floating-point exponent within the block.

.. c:member:: int zfp_stream.minexp

  The smallest absolute bit plane number encoded (applies to floating-point
  data only; this parameter is ignored for integer data).  The place value of
  each transform coefficient bit depends on the common floating-point exponent,
  *e*, that scales the integer coefficients.  If the most significant
  coefficient bit has place value 2\ :sup:`e`, then the number of bit planes
  encoded is (one plus) the difference between *e* and
  :c:member:`zfp_stream.minexp`.  As an analogy, consider representing
  currency in decimal.  Setting :c:member:`zfp_stream.minexp` to -2 would,
  if generalized to base 10, ensure that amounts are represented to cent
  accuracy, i.e., in units of 10\ :sup:`-2` = $0.01.  This parameter governs
  the *absolute error* in :ref:`fixed-accuracy mode <mode-fixed-accuracy>`.
  Note that to achieve a certain accuracy in the decompressed values, the
  :c:member:`zfp_stream.minexp` value has to be conservatively lowered since
  |zfp|'s inverse transform may magnify the error (see also
  :ref:`FAQs #20-22 <q-relerr>`).

Care must be taken to allow all constraints to be met, as encoding terminates as soon as a single constraint is violated (except :c:member:`zfp_stream.minbits`, which is satisfied at the end of encoding by padding zeros).

As mentioned above, other combinations of constraints can be used. For example, to ensure that the compressed stream is not larger than the uncompressed one, or that it fits within the amount of memory allocated, one may in conjunction with other constraints set

maxbits = 4^d * CHAR_BIT * sizeof(Type)

where Type is either float or double. The minbits parameter is useful only in fixed-rate mode; when minbits = maxbits, zero-bits are padded to blocks that compress to fewer than maxbits bits.

The effects of the above four parameters are best explained in terms of the three main compression modes supported by |zfp|, described below.

.. index::
   single: Compression mode; Fixed-rate mode
   single: Rate

In fixed-rate mode, each d-dimensional compressed block of |4powd| values is stored using a fixed number of bits given by the parameter :c:member:`zfp_stream.maxbits`. This number of compressed bits per block is amortized over the |4powd| values to give a rate in bits per value:

rate = maxbits / 4^d

This rate is specified in the :ref:`zfp executable <zfpcmd>` via the :option:`-r` option, and programmatically via :c:func:`zfp_stream_set_rate`, as a floating-point value. Fixed-rate mode can also be achieved via the expert mode interface by setting

minbits = maxbits = (1 << (2 * d)) * rate
maxprec = ZFP_MAX_PREC
minexp = ZFP_MIN_EXP

Note that each block stores a bit to indicate whether the block is empty, plus a common exponent. Hence :c:member:`zfp_stream.maxbits` must be at least 9 for single precision and 12 for double precision.

Fixed-rate mode is needed to support random access to blocks, and also is the mode used in the implementation of |zfp|'s :ref:`compressed arrays <arrays>`. Fixed-rate mode also ensures a predictable memory/storage footprint, but usually results in far worse accuracy per bit than the variable-rate fixed-precision and fixed-accuracy modes.

.. index::
   single: Compression mode; Fixed-precision mode

In fixed-precision mode, the number of bits used to encode a block may vary, but the number of bit planes (i.e., the precision) encoded for the transform coefficients is fixed. To achieve the desired precision, use option :option:`-p` with the :ref:`zfp executable <zfpcmd>` or call :c:func:`zfp_stream_set_precision`. In expert mode, fixed precision is achieved by specifying the precision in :c:member:`zfp_stream.maxprec` and fully relaxing the size constraints, i.e.,

minbits = ZFP_MIN_BITS
maxbits = ZFP_MAX_BITS
maxprec = precision
minexp = ZFP_MIN_EXP

Fixed-precision mode is preferable when relative rather than absolute errors matter.

.. index::
   single: Compression mode; Fixed-accuracy mode

In fixed-accuracy mode, all transform coefficient bit planes up to a minimum bit plane number are encoded. (The actual minimum bit plane is not necessarily :c:member:`zfp_stream.minexp`, but depends on the dimensionality, d, of the data. The reason for this is that the inverse transform incurs range expansion, and the amount of expansion depends on the number of dimensions.) Thus, :c:member:`zfp_stream.minexp` should be interpreted as the base-2 logarithm of an absolute error tolerance. In other words, given an uncompressed value, f, and a reconstructed value, g, the absolute difference | f |minus| g | is at most 2^minexp. (Note that it is not possible to guarantee error tolerances smaller than machine epsilon relative to the largest value within a block.) This error tolerance is not always tight (especially for 3D and 4D arrays), but can conservatively be set so that even for worst-case inputs the error tolerance is respected. To achieve fixed accuracy to within 'tolerance', use option :option:`-a` with the :ref:`zfp executable <zfpcmd>` or call :c:func:`zfp_stream_set_accuracy`. The corresponding expert mode parameters are:

minbits = ZFP_MIN_BITS
maxbits = ZFP_MAX_BITS
maxprec = ZFP_MAX_PREC
minexp = floor(log2(tolerance))

As in fixed-precision mode, the number of bits used per block is not fixed but is dictated by the data. Use tolerance = 0 to achieve near-lossless compression (see :ref:`mode-reversible` for guaranteed lossless compression). Fixed-accuracy mode gives the highest quality (in terms of absolute error) for a given compression rate, and is preferable when random access is not needed.

.. index::
   single: Compression mode; Reversible mode
   single: Lossless compression

As of |zfp| |revrelease|, reversible (lossless) compression is supported. As with the other compression modes, each block is compressed and decompressed independently, but reversible mode uses a different compression algorithm that ensures a bit-for-bit identical reconstruction of integer and floating-point data. For IEEE-754 floating-point data, reversible mode preserves special values such as subnormals, infinities, NaNs, and positive and negative zero.

The expert mode parameters corresponding to reversible mode are:

minbits = ZFP_MIN_BITS
maxbits = ZFP_MAX_BITS
maxprec = ZFP_MAX_PREC
minexp < ZFP_MIN_EXP

Reversible mode is enabled via :c:func:`zfp_stream_set_reversible` and through the :option:`-R` command-line option in the :ref:`zfp executable <zfpcmd>`. It is supported by both the low- and high-level interfaces and by the serial and OpenMP execution policies, but it is not yet implemented in CUDA.