OVERVIEW

zfp consists of three distinct components: (1) a set of low-level C codecs
for compressing and decompressing block subsets of one-, two-, and three-
dimensional single- and double-precision arrays; (2) a set of corresponding
C++ compressed array classes that support random access; and (3) a high-level
C interface for compressing and decompressing entire floating-point arrays.

The compression codecs operate on individual d-dimensional blocks of size
4^d, e.g. 4 values in 1D, 4x4 = 16 values in 2D, and 4x4x4 = 64 values in
3D.  The block being compressed need not be stored contiguously but can
be processed by specifying regular strides in each dimension.  This is
useful if the block is initially stored uncompressed as part of a larger
array.

The array classes represent an entire array of floating-point values as
a collection of compressed blocks, each whose compressed size in number
of bits is fixed and specified by the user.  The array classes cache
uncompressed blocks to reduce the number of compression and decompression
calls.  Whenever an array value is read, the corresponding block is first
looked up in the cache, and if found the uncompressed value is returned.
Otherwise the block is first decompressed and stored in the cache.
Whenever an array element is written (whether actually modified or not),
a "dirty bit" is set with its cached block to indicate that the block
must be compressed back to persistent storage when evicted from the cache.

The libzfp C interface is useful for quickly compressing and archiving
large floating-point arrays of arbitrary dimensions without having to
understand the technical details of the compression algorithm and codec.
This library comes with utility functions for specifying the compression
rate, precision, or accuracy of the compressed data.

All code examples below are for 3D arrays of doubles, but it should be
clear how to modify the function calls for single precision and for 1D
or 2D arrays.


GENERAL DESIGN AND LIMITATIONS

The zfp API has been designed to facilitate integration with existing
applications.  After initial array declaration, a zfp array can often
be used in place of a regular C/C++ array or STL vector, e.g. using flat
indexing via a[index] or using multidimensional indexing via a(i),
a(i, j), or a(i, j, k).  There are, however, some important differences.
For instance, it is not possible to take the address of an array element,
i.e. constructions like &a[i] and a + i are not allowed.  Moreover, the
operators [] and () do not return regular C++ references.  Instead, a
proxy reference class is used (similar to how STL bit vectors are
implemented).  These proxy references can, however, safely be passed to
functions and used where regular references can.

zfp does not support special floating-point values like infinities and
NaNs, although denormalized numbers are handled correctly.  Similarly,
because the compressor assumes that the array values vary smoothly,
using finite but large values like HUGE_VAL in place of infinities is
not advised, as this will introduce large errors in smaller values
within the same block.  Future extensions will provide support for a
bit mask to mark the presence of non-values.

The zfp C++ classes are implemented entirely as header files and make
extensive use of C++ templates to reduce code redundancy.  Most classes
are wrapped in the 'zfp' namespace.


API OVERVIEW

The documentation is divided into three parts: the high-level libzfp
library; the low-level compression codecs; and the compressed array
classes (in that order).  Users interested only in the compressed arrays,
which do not directly expose anything related to compression other than
compression rate control, may safely skip the next two sections.


ZFP HIGH-LEVEL C INTERFACE

Users concerned only with storing their floating-point data compressed may
use zfp as a black box that maps a possibly non-contiguous floating-point
array to a compressed bit stream.  The intent of libzfp is to provide both
a high- and low-level interface to the compressor that can be called from
both C and C++ (and possibly other languages).  libzfp supports strided
access, e.g. for compressing vector fields one scalar at a time, or for
compressing arrays of structs.

Consider compressing the 3D C/C++ array

  // define an uncompressed array
  double a[nz][ny][nx];

where nx, ny, and nz can be any positive dimensions.  To invoke the libzfp
compressor, the dimensions and type must first be specified in a zfp_field
parameter object that encapsulates the type, size, and memory layout of the
array:

  // allocate metadata for the 3D array a[nz][ny][nx]
  uint dims = 3;
  zfp_type type = zfp_type_double;
  zfp_field* field = zfp_field_3d(&a[0][0][0], type, nx, ny, nz);

For single-precision data, use zfp_type_float.  Note that the high-level
API does not support integer arrays (zfp_type_int32 and zfp_type_int64).
Such arrays must be compressed via the low-level interface.

Functions similar to zfp_field_3d exist for declaring 1D and 2D arrays.
If the dimensionality of the array is unknown at this point, then a generic
zfp_field_alloc() call can be made to just allocate a zfp_field struct,
which can be filled in later using the zfp_field_set_* functions.  If the
array is non-contiguous, then zfp_field_set_stride_3d should be called.

The zfp_field parameter object holds information about the uncompressed
array.  To specify the compressed array, a zfp_stream object must be
allocated:

  // allocate metadata for a compressed stream
  zfp_stream* zfp = zfp_stream_open(NULL);

We may now specify the rate, precision, or accuracy (see the README file
for more details on the meaning of these parameters):

  // set compression mode and parameters
  zfp_stream_set_rate(zfp, rate, type, dims, 0);
  zfp_stream_set_precision(zfp, precision, type);
  zfp_stream_set_accuracy(zfp, tolerance, type);

Note that only one of these three functions should be called.  The return
value from these functions gives the actual rate, precision, or tolerance,
and may differ slightly from the argument passed due to constraints imposed
by the compressor, e.g. each block must be stored using a whole number of
bits at least as large as the number of bits in the floating-point exponent;
the precision cannot exceed the number of bits in a floating-point value
(i.e. 32 for single and 64 for double precision); and the tolerance must
be a (possibly negative) power of two.

The compression parameters have now been specified, but before compression
can occur a buffer large enough to hold the compressed bit stream must be
allocated.  Another utility function exists for estimating how many bytes
are needed:

  // allocate buffer for compressed data
  size_t bufsize = zfp_stream_maximum_size(zfp, field);
  uchar* buffer = new uchar[bufsize];

Note that zfp_stream_maximum_size returns the smallest buffer size
necessary to safely compress the data--the actual compressed size may be
smaller.  If the members of zfp and field are for whatever reason not
initialized correctly, then zfp_stream_maximum_size returns 0.

Before compression can commence, we must associate the allocated buffer
with a bit stream used by the compressor to read and write bits:

  // associate bit stream with allocated buffer
  bitstream* stream = stream_open(buffer, bufsize);
  zfp_stream_set_bit_stream(zfp, stream);

Finally, the array is compressed as follows:

  // compress entire array
  size_t size = zfp_compress(zfp, field);

The return value is the actual number of bytes of compressed storage, and
as already mentioned, size <= bufsize.  If size = 0, then the compressor
failed.  Since zfp 0.5.0, the compressor does not rewind the bit stream
before compressing, which allows multiple fields to be compressed one
after the other.  The return value from zfp_compress is always the total
number of bytes of compressed storage so far relative to the memory
location pointed to by 'buffer'.

To decompress the data, the field and compression parameters must be
initialized with the same values as used for compression, either via
the same sequence of function calls as above, or by recording these
fields and setting them directly.  Metadata such as array dimensions and
compression parameters are by default not stored in the compressed stream.
It is up to the caller to store this information, either separately from
the compressed data, or via the zfp_write_header and zfp_read_header calls.
These calls allow the user to specify what information to store in the
header, including a 'magic' format identifier, the field type and
dimensions, and the compression parameters (see the ZFP_HEADER_* macros).

In addition to this initialization, the bit stream has to be rewound to
the beginning:

  // rewind compressed stream and decompress array
  zfp_stream_rewind(zfp);
  int success = zfp_decompress(zfp, field);

The return value is zero if the decompressor failed.


ZFP LOW-LEVEL COMPRESSION AND DECOMPRESSION CODEC

For applications that wish to compress or decompress portions of an array
on demand, a low-level interface is available.  Since this API is useful
primarily for supporting random access, the user also needs to manipulate
the bit stream (see inc/bitstream.h), e.g. to position the bit pointer
to where data is to be read or written.  Please be advised that the bit
stream functions have been optimized for speed, and do not check for
buffer overruns or other types of programmer error.

Like the high-level API, the low-level API also makes use of the zfp_stream
parameter object (see section above) to specify compression parameters and
storage, but does not encapsulate array metadata in a zfp_field object.
Functions exists for encoding and decoding complete or partial blocks, with
or without strided access.  In non-strided mode, the uncompressed block to
be encoded or decoded is assumed to be stored contiguously.  For example,

  // compress a single contiguous block
  double block[4 * 4 * 4] = { /* some set of values */ };
  uint bits = zfp_encode_block_double_3(zfp, block);

The return value is the number of bits of compressed storage for the block.
For fixed-rate streams, if random access is desired, then the stream should
also be flushed after each block is encoded:

  // flush any buffered bits
  zfp_stream_flush(zfp);

This flushing should be done only after the last block has been compressed in
fixed-precision and fixed-accuracy mode, or when random access is not needed
in fixed-rate mode.

The block above could also have been compressed as follows using strides:

  // compress a single contiguous block using strides
  double block[4][4][4] = { /* some set of values */ };
  int sx = &block[0][0][1] - &block[0][0][0]; // x stride =  1
  int sy = &block[0][1][0] - &block[0][0][0]; // y stride =  4
  int sz = &block[1][0][0] - &block[0][0][0]; // z stride = 16
  uint bits = zfp_encode_block_strided_double_3(zfp, block, sx, sy, sz);

The strides are measured in number of scalars, not in bytes.

For partial blocks, e.g. near the boundaries of arrays whose dimensions
are not multiples of four, there are corresponding functions that accept
parameters (nx, ny, nz) to specify the actual block dimensions, with
1 <= nx, ny, nz <= 4.  Corresponding functions exist for decompression.

To position a bit stream for reading (decompression), use

  // position the stream at given bit offset for reading
  stream_rseek(stream, offset);

where the offset is measured in number of bits from the beginning of the
stream.  For writing (compression), a corresponding call exists:

  // position the stream at given bit offset for writing
  stream_wseek(stream, offset);

Note that it is possible to decompress fewer bits than are stored with a
compressed block to quickly obtain an approximation.  This is done by
setting zfp->maxbits to fewer bits than used during compression, e.g. to
decompress only the first 256 bits of each block:

  // modify decompression parameters to decode 256 bits per block
  uint maxbits;
  uint maxprec;
  int minexp;
  zfp_stream_params(zfp, NULL, &maxbits, &maxprec, &minexp);
  assert(maxbits >= 256);
  zfp_stream_set_params(zfp, 256, 256, maxprec, minexp);

This feature may be combined with progressive decompression, as discussed
further in the FAQ.


COMPRESSED ARRAYS

Currently there are six array classes for 1D, 2D, and 3D arrays, each of
which can represent single- or double-precision values.  Although these
arrays store values in a form different from conventional single- and
double-precision floating point, the user interacts with the arrays via
floats and doubles.

The description below is for 3D arrays of doubles--the necessary changes
for other array types should be obvious.  To declare and zero initialize
an array, use

  // declare nx * ny * nz array of compressed doubles
  zfp::array3<double> a(nx, ny, nz, rate);

This declaration is conceptually equivalent to

  double a[nz][ny][nx] = {};

or

  std::vector<double> a(nx * ny * nz, 0.0);

but with the user specifying the amount of storage used.  (A predefined type
array3d also exists, while the suffix 'f' is used for floats.)  Note that
the array dimensions can be arbitrary, and need not be multiples of four
(see above for a discussion of incomplete blocks).  The 'rate' argument
specifies how many bits per value (amortized) to store in the compressed
representation.  By default the block size is restricted to a multiple of
64 bits, and therefore the rate argument can be specified in increments of
64 / 4^d bits in d dimensions, i.e.

  1D arrays: 16-bit granularity
  2D arrays: 4-bit granularity
  3D arrays: 1-bit granularity

For finer granularity, the BITSTREAM_WORD_TYPE macro needs to be set to a
type narrower than 64 bits, e.g. if set to uint8 the rate granularity
becomes 8 / 4^d bits in d dimensions, or

  1D arrays: 2-bit granularity
  2D arrays: 1/2-bit granularity
  3D arrays: 1/8-bit granularity

Note that finer granularity implies lower performance.  Also note that
because the arrays are stored compressed, their effective precision is
likely to be higher than the user-specified rate.

The array can also optionally be initialized from an existing contiguous
floating-point array stored at 'pointer' with an x stride of 1, y stride
of nx, and z stride of nx * ny:

  // declare and initialize 3D array of doubles
  zfp::array3d a(nx, ny, nz, precision, pointer, cache_size);

The 'cache_size' argument specifies the minimum number of bytes to allocate
for the cache of uncompressed blocks (see the section on Caching below for
more details).

If not already initialized, a function set() can be used to copy uncompressed
data to the compressed array:

  const double* pointer; // pointer to uncompressed, initialized data
  a.set(pointer); // initialize compressed array with floating-point data

Similarly, a get() function exists for retrieving uncompressed data:

  double* pointer; // pointer to where to write uncompressed data
  a.get(pointer); // decompress and store the array at pointer

The compressed representation of an array can also be queried or initialized 
directly without having to convert to/from its floating-point representation:

  size_t bytes = compressed_size(); // number of bytes of compressed storage
  uchar* compressed_data(); // pointer to compressed data

The array can through this pointer be initialized from offline compressed
storage, but only after its dimensions and rate have been specified (see
above).  For this to work properly, the cache must first be emptied via a
clear_cache() call (see below).

Through operator overloading, the array can be accessed in one of two ways.
For read accesses, use

  double value = a[index]; // fetch value with given flat array index
  double value = a(i, j, k); // fetch value with 3D index (i, j, k)

These access the same value if and only if index = i + nx * (j + ny * k).
Note that 0 <= i < nx, 0 <= j < ny, and 0 <= k < nz, and i varies faster
than j, which varies faster than k.

Array values may be written and updated using the usual set of C++ assignment
and compound assignment operators.  For example:

  a[index] = value; // set value at flat array index
  a(i, j, k) += value; // increment value with 3D index (i, j, k)

Whereas one might expect these operators to return a (non-const) reference
to an array element, this would allow seating a reference to a value that
currently is cached but is transient, which could be unsafe.  Moreover,
this would preclude detecting when an array element is modified.  Therefore,
the return type of both operators [] and () is a proxy reference class,
similar to std::vector<bool>::reference from the STL library.  Because
read accesses to a mutable object cannot call the const-qualified accessor,
a proxy reference may be returned even for read calls, e.g. in

  a[i - 1] = a[i];

the array a clearly must be mutable to allow assignment to a[i - 1], and
therefore the read access a[i] returns type zfp::array3d::reference.  The
value associated with the read access is obtained via an implicit conversion.

Array dimensions (nx, ny, nz) can be queried using these functions:

  size_t size(); // total number of elements nx * ny * nz
  uint size_x(); // nx
  uint size_y(); // ny
  uint size_z(); // nz

The array dimensions can also be changed dynamically, e.g. if not known
at declaration time, using

  void resize(uint nx, uint ny, uint nz, bool clear = true);

When clear = true, the array is explicitly zeroed.  In either case, all
previous contents of the array are lost.  If nx = ny = nz = 0, all storage
is freed.

Finally, the rate supported by the array may be queried via

  double rate(); // number of compressed bits per value

and changed using

  void set_rate(rate); // change rate

This also destroys prior contents.


CACHING

As mentioned above, the array class maintains a software write-back cache
of at least one uncompressed block.  When a block in this cache is evicted
(e.g. due to a conflict), it is compressed back to permanent storage only
if it has previously been modified.

The size cache to use is specified by the user, and is an important
parameter that needs careful consideration in order to balance the extra
memory usage, performance, and quality (recall that data loss is incurred
only when a block is evicted from the cache and compressed).  Although the
best choice varies from one application to another, we suggest allocating
at least two layers of blocks (2 * (nx / 4) * (ny / 4) blocks) for
applications that stream through the array and perform stencil computations
such as gathering data from neighboring elements.  This allows limiting the
cache misses to compulsory ones.  If the cache_size parameter is set to
zero bytes, then this default of two layers is used.

The cache size can be set during construction, or can be set at a later
time via

  void set_cache_size(bytes); // change cache size

Note that if bytes = 0, then the array dimensions must have already been
specified for the default size to be computed correctly.  When the cache
is resized, it is first flushed if not already empty.  The cache can
also be flushed explicitly if desired by calling

  void flush_cache(); // empty cache by first compressing any modified blocks

To empty the cache without compressing any cached data, call

  void clear_cache(); // empty cache without compression

To query the byte size of the cache, use

  size_t cache_size(); // actual cache size in bytes