Description:
------------
The following functions are available since PHP 7.0.0 and quoted in its changelog, but their description is still missing from the manual; I add here my findings as guessed from the C source code and from the ZLIB manual in a DocBlock-like format:


/**
 * Initialize an incremental deflate context using the specified encoding.
 * Note that the 'window' option here only sets the window size of the algorithm,
 * differently from the zlib filters where the same parameter also set the
 * encoding to use; the encoding must be set with the $encoding parameter.
 * Limitation: there is no currently way to set the header informations on a
 * GZIP compressed stream, which are set as follows: GZIP signature (“\x1f\x8B”);
 * compression method (“\x08” == DEFLATE); 6 zero bytes; the operating system
 * set to the current system (“\x00” = Windows, “\x03” = Unix, etc.).
 * @param int $encoding One of:
 * ZLIB_ENCODING_RAW (DEFLATE algorithm as per RFC 1951),
 * ZLIB_ENCODING_DEFLATE (ZLIB compress algorithm as per RFC 1950) or
 * ZLIB_ENCODING_GZIP (GZIP algorithm as per RFC 1952).
 * @param int[string] $options Allowed entries are:<br>
 * 'level': compression level, range -1..9, default -1;<br>
 * 'memory': compression memory level, range 1..9, default 8;<br>
 * 'window': zlib window size (logarithm), range 8..15, default 15;<br>
 * 'strategy': one of ZLIB_FILTERED, ZLIB_HUFFMAN_ONLY, ZLIB_RLE, ZLIB_FIXED
 * or ZLIB_DEFAULT_STRATEGY (default);
 * 'dictionary': a string or an array of strings of the preset dictionary
 * (default: no preset dictionary).
 * @return resource Deflate context, or FALSE on error.
 * @triggers E_WARNING Invalid option. Failed to create the context.
 */
function deflate_init($encoding, $options = array());


/**
 * Incrementally deflate data in the specified context.
 * @param resource $context Context created with deflate_init().
 * @param string $data Chunk of data to compress.
 * @param int $flush_mode One of: ZLIB_BLOCK, ZLIB_NO_FLUSH, ZLIB_PARTIAL_FLUSH,
 * ZLIB_SYNC_FLUSH (default), ZLIB_FULL_FLUSH, ZLIB_FINISH. Normally you will
 * want to set ZLIB_NO_FLUSH here to maximize compression, and ZLIB_FINISH to
 * terminate with the last chunk of data. See the ZLIB manual at
 * {@link http://www.zlib.net/manual.html} for a detailed description of
 * these constants.
 * @return string Chunk of dompressed data, or FALSE on error.
 * @triggers E_WARNING Invalid parameters.
 */
function deflate_add($context, $data, $flush_mode = ZLIB_SYNC_FLUSH);


/**
 * Initialize an incremental inflate context with the specified encoding.
 * @param int $encoding One of:
 * ZLIB_ENCODING_RAW (DEFLATE algorithm as per RFC 1951),
 * ZLIB_ENCODING_DEFLATE (ZLIB compress algorithm as per RFC 1950) or
 * ZLIB_ENCODING_GZIP (GZIP algorithm as per RFC 1952).
 * @param int[string] $options Allowed entries are:<br>
 * 'level': compression level, range -1..9, default -1;<br>
 * 'memory': compression memory level, range 1..9, default 8;<br>
 * 'window': zlib window size (logarithm), range 8..15, default 15;<br>
 * 'strategy': one of ZLIB_FILTERED, ZLIB_HUFFMAN_ONLY, ZLIB_RLE, ZLIB_FIXED
 * or ZLIB_DEFAULT_STRATEGY (default);
 * 'dictionary': a string or an array of strings of the preset dictionary
 * (default: no preset dictionary).
 * @return resource Inflate context, or FALSE on error.
 * @triggers E_WARNING Invalid encoding. Invalid option. Failed to allocate
 * the context.
 */
function inflate_init($encoding, $options = array());

/**
 * Incrementally inflate encoded data in the specified context.
 * Limitation: header informations from GZIP compressed data are not made
 * available.
 * @param resource $context Context created with inflate_init().
 * @param string $encoded_data Chunk of compressed data.
 * @param int $flush_mode One of: ZLIB_BLOCK, ZLIB_NO_FLUSH, ZLIB_PARTIAL_FLUSH,
 * ZLIB_SYNC_FLUSH (default), ZLIB_FULL_FLUSH, ZLIB_FINISH. Normally you will
 * want to set ZLIB_NO_FLUSH to maximize speed, and ZLIB_FINISH to
 * terminate with the last block of data. See the ZLIB manual at
 * {@link http://www.zlib.net/manual.html} for a detailed description of
 * these constants.
 * @return string Chunk of decompressed data, or FALSE on error.
 * @triggers E_WARNING Invalid parameters. Inflating this data requires a preset
 * dictionary, please specify it in the options array of inflate_init().
 * Corrupted compressed stream or invalid checksum (whenever available).
 */
function inflate_add($context, $encoded_data, $flush_mode = ZLIB_SYNC_FLUSH);


A very simple example of use:

// Performs GZIP compression:
$deflateContext = deflate_init(ZLIB_ENCODING_GZIP);
$compressed = deflate_add($deflateContext, "Data to compress", ZLIB_NO_FLUSH);
$compressed .= deflate_add($deflateContext, ", more data", ZLIB_NO_FLUSH);
$compressed .= deflate_add($deflateContext, ", and even more data!", ZLIB_FINISH);

// Performs GZIP decompression:
$inflateContext = inflate_init(ZLIB_ENCODING_GZIP);
$uncompressed = inflate_add($inflateContext, $compressed, ZLIB_NO_FLUSH);
$uncompressed .= inflate_add($inflateContext, NULL, ZLIB_FINISH);
echo $uncompressed;
# --> Data to compress, more data, and even more data!