Tutorial

This tutorial provides examples that illustrate how to use the zfp library and compressed arrays, and includes code snippets that show the order of declarations and function calls needed to use the compressor.

This tutorial 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.

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, 2D, or 4D arrays.

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.

Note

In multidimensional arrays, the order in which dimensions are specified is important. In zfp, the memory layout convention is such that x varies faster than y, which varies faster than z, and hence x should map to the innermost (rightmost) array dimension in a C array and to the leftmost dimension in a Fortran array. Getting the order of dimensions right is crucial for good compression and accuracy. See the discussion of dimensions and strides for further information.

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. As of version 0.5.1, the high-level API also supports integer arrays (zfp_type_int32 and zfp_type_int64). See FAQs #8 and #9 regarding integer compression.

Functions similar to zfp_field_3d() exist for declaring 1D, 2D, and 4D 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 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 Compression Modes 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);
zfp_stream_set_accuracy(zfp, tolerance);

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);

Compression can be accelerated via OpenMP multithreading (since zfp 0.5.3) and CUDA (since zfp 0.5.4). To enable OpenMP parallel compression, call:

if (!zfp_stream_set_execution(zfp, zfp_exec_omp)) {
  // OpenMP not available; handle error
}

See the section Parallel Execution for further details on how to configure zfp and its run-time parameters for parallel compression.

Finally, the array is compressed as follows:

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

If the stream was rewound before calling zfp_compress(), 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 separate from the compressed data, or via the zfp_write_header() and zfp_read_header() calls, which should precede the corresponding zfp_compress() and zfp_decompress() calls, respectively. 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 (before reading the header and decompressing the data):

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

The return value is zero if the decompressor failed.

Simple Example

Tying it all together, the code example below (see also the simple program) shows how to compress a 3D array double array[nz][ny][nx]:

// input: (void* array, int nx, int ny, int nz, double tolerance)

// initialize metadata for the 3D array a[nz][ny][nx]
zfp_type type = zfp_type_double;                          // array scalar type
zfp_field* field = zfp_field_3d(array, type, nx, ny, nz); // array metadata

// initialize metadata for a compressed stream
zfp_stream* zfp = zfp_stream_open(NULL);                  // compressed stream and parameters
zfp_stream_set_accuracy(zfp, tolerance);                  // set tolerance for fixed-accuracy mode
//  zfp_stream_set_precision(zfp, precision);             // alternative: fixed-precision mode
//  zfp_stream_set_rate(zfp, rate, type, 3, 0);           // alternative: fixed-rate mode

// allocate buffer for compressed data
size_t bufsize = zfp_stream_maximum_size(zfp, field);     // capacity of compressed buffer (conservative)
void* buffer = malloc(bufsize);                           // storage for compressed stream

// associate bit stream with allocated buffer
bitstream* stream = stream_open(buffer, bufsize);         // bit stream to compress to
zfp_stream_set_bit_stream(zfp, stream);                   // associate with compressed stream
zfp_stream_rewind(zfp);                                   // rewind stream to beginning

// compress array
size_t zfpsize = zfp_compress(zfp, field);                // return value is byte size of compressed stream

Low-Level C Interface

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, 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 previous section) to specify compression parameters and storage, but does not encapsulate array metadata in a zfp_field object. Functions exist 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 write 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, and nz to specify the actual block dimensions, with 1 ≤ nx, ny, nz ≤ 4. Corresponding functions exist for decompression. Such partial blocks typically do not compress as well as full blocks and should be avoided if possible.

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. For example, 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 FAQ #13.

Compressed C++ Arrays

The zfp compressed array API, which currently supports 1D, 2D, and 3D (but not 4D) arrays, 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], nested indexing a[k][j][i] (via nested views), or using multidimensional indexing via a(i), a(i, j), or a(i, j, k). There are, however, some important differences. For instance, applications that rely on addresses or references to array elements may have to be modified to use special proxy classes that implement pointers and references; see Limitations.

zfp’s compressed arrays do not support special floating-point values like infinities and NaNs, although subnormal 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. These classes are wrapped in the zfp namespace.

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] = { 0.0 };

or using STL vectors

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

but with the user specifying the amount of storage used via the rate parameter. (A predefined type array3d also exists, while the suffix ‘f’ is used for floats.)

Note

In multidimensional arrays, the order in which dimensions are specified is important. In zfp, the memory layout convention is such that x varies faster than y, which varies faster than z, and hence x should map to the innermost (rightmost) array dimension in a C array and to the leftmost dimension in a Fortran array. Getting the order of dimensions right is crucial for good compression and accuracy. See the discussion of dimensions and strides for further information.

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 BIT_STREAM_WORD_TYPE macro needs to be set to a type narrower than 64 bits during compilation of libzfp, 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 usually implies slightly 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, rate, pointer, cache_size);

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

As of zfp 0.5.3, entire arrays may be copied via the copy constructor or assignment operator:

zfp::array3d b(a); // declare array b to be a copy of array a
zfp::array3d c; // declare empty array c
c = a; // copy a to c

Copies are deep and have value (not reference) semantics. In the above example, separate storage for b and c is allocated, and subsequent modifications to b and c will not modify a.

If not already initialized, a function array::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, an array::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 array::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.

zfp 0.5.4 adds views to arrays, which among other things can be used to perform nested indexing:

zfp::array3d::nested_view v(&a);
double value = v[k][j][i];

A view is a shallow copy of an array or a subset of an array.

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. For example, in

a[i] = a[i + 1];

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

Array dimensions nx, ny, and 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 time of construction, 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.

As of zfp 0.5.2, iterators and proxy objects for pointers and references are supported. Note that the decompressed value of an array element exists only intermittently, when the decompressed value is cached. It would not be safe to return a double& reference or double* pointer to the cached but transient value since it may be evicted from the cache at any point, thus invalidating the reference or pointer. Instead, zfp provides proxy objects for references and pointers that guarantee persistent access by referencing elements by array object and index. These classes perform decompression on demand, much like how Boolean vector references are implemented in the STL.

Iterators for 1D arrays support random access, while 2D and 3D array iterators are merely forward (sequential) iterators. All iterators ensure that array values are visited one block at a time, and are the preferred way of looping over array elements. Such block-by-block access is especially useful when performing write accesses since then complete blocks are updated one at a time, thus reducing the likelihood of a partially updated block being evicted from the cache and compressed, perhaps with some values in the block being uninitialized. Here is an example of initializing a 3D array:

for (zfp::array3d::iterator it = a.begin(); it != a.end(); it++) {
  int i = it.i();
  int j = it.j();
  int k = it.k();
  a(i, j, k) = some_function(i, j, k);
}

Pointers to array elements are available via a special pointer class. Such pointers may be a useful way of passing (flattened) zfp arrays to functions that expect uncompressed arrays, e.g., by using the pointer type as template argument. For example:

template <typename double_ptr>
void sum(double_ptr p, int count)
{
  double s = 0;
  for (int i = 0; i < count; i++)
    s += p[i];
  return s;
}

Then the following are equivalent:

// sum of STL vector elements (double_ptr == double*)
std::vector<double> vec(nx * ny * nz, 0.0);
double vecsum = sum(&vec[0], nx * ny * nz);

// sum of zfp array elements (double_ptr == zfp::array3d::pointer)
zfp::array3<double> array(nx, ny, nz, rate);
double zfpsum = sum(&array[0], nx * ny * nz);

As another example,

for (zfp::array1d::pointer p = &a[0]; p - &a[0] < a.size(); p++)
  *p = 0.0;

initializes a 1D array to all-zeros. Pointers visit arrays in standard row-major order, i.e.

&a(i, j, k) == &a[0] + i + nx * (j + ny * k)
            == &a[i + nx * (j + ny * k)]

where &a(i, j, k) and &a[0] are both of type array3d::pointer. Thus, iterators and pointers do not visit arrays in the same order, except for the special case of 1D arrays. Unlike iterators, pointers support random access for arrays of all dimensions and behave very much like float* and double* built-in pointers.

Proxy objects for array element references have been supported since the first release of zfp, and may for instance be used in place of double&. Iterators and pointers are implemented in terms of references.

The following table shows the equivalent zfp type to standard types when working with 1D arrays:

double&                         zfp::array1d::reference
double*                         zfp::array1d::pointer
std::vector<double>::iterator   zfp::array1d::iterator

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 was modified while stored in the cache.

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 accuracy (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 a default size of √n blocks is used, where n is the total number of blocks in the array.

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