Libpng 1.4.0beta76 - August 21, 2009 This is not intended to be a public release. It will be replaced within a few weeks by a public version or by another test version. Files available for download: Source files with LF line endings (for Unix/Linux) and with a "configure" script 1.4.0beta76.tar.xz (LZMA-compressed, recommended) 1.4.0beta76.tar.gz 1.4.0beta76.tar.bz2 Source files with LF line endings (for Unix/Linux) without the "configure" script 1.4.0beta76-no-config.tar.xz (LZMA-compressed, recommended) 1.4.0beta76-no-config.tar.gz 1.4.0beta76-no-config.tar.bz2 Source files with CRLF line endings (for Windows), without the "configure" script lp140b76.zip lp140b76.tar.bz2 Other information: 1.4.0beta76-README.txt 1.4.0beta76-KNOWNBUGS.txt 1.4.0beta76-LICENSE.txt 1.4.0beta76-Y2K-compliance.txt Changes since the last public release (1.2.10): version 1.2.10beta1 [April 15, 2006] Renamed "config.h" to "png_conf.h" and revised Makefile.am to add -DPNG_BUILDING_LIBPNG to compile directive, and modified pngconf.h to include png_conf.h only when PNG_BUILDING_LIBPNG is defined. version 1.2.10beta2 [April 15, 2006] Manually updated Makefile.in and configure. Changed png_conf.h.in back to config.h. version 1.2.10beta3 [April 15, 2006] Change png_conf.h back to config.h in pngconf.h. version 1.2.10beta4 [April 16, 2006] Change PNG_BUILDING_LIBPNG to PNG_CONFIGURE_LIBPNG in config/Makefile*. version 1.2.10beta5 [April 16, 2006] Added a configure check for compiling assembler code in pnggccrd.c version 1.2.10beta6 [April 17, 2006] Revised the configure check for pnggccrd.c Moved -DPNG_CONFIGURE_LIBPNG into @LIBPNG_DEFINES@ Added @LIBPNG_DEFINES@ to arguments when building libpng.sym version 1.2.10beta7 [April 18, 2006] Change "exec_prefix=$prefix" to "exec_prefix=$(prefix)" in makefiles. version 1.2.10rc1 [April 19, 2006] Ensure pngconf.h doesn't define both PNG_USE_PNGGCCRD and PNG_USE_PNGVCRD Fixed "LN_FS" typo in makefile.sco and makefile.solaris. version 1.2.10rc2 [April 19, 2006] Added a backslash between -DPNG_CONFIGURE_LIBPNG and -DPNG_NO_ASSEMBLER_CODE in configure.ac Made the configure warning about versioned symbols less arrogant. version 1.2.10rc3 [April 20, 2006] Added a note in libpng.txt that png_set_sig_bytes(8) can be used when writing an embedded PNG without the 8-byte signature. version 1.4.0beta1 [April 20, 2006] Enabled iTXt support (changes png_struct, thus requires so-number change). Cleaned up PNG_ASSEMBLER_CODE_SUPPORTED vs PNG_MMX_CODE_SUPPORTED Eliminated PNG_1_0_X and PNG_1_2_X macros. Removed deprecated functions png_read_init, png_write_init, png_info_init, png_permit_empty_plte, png_set_gray_1_2_4_to_8, and removed the deprecated macro PNG_MAX_UINT. Moved "PNG_INTERNAL" parts of png.h and pngconf.h into pngintrn.h Removed many WIN32_WCE #ifdefs (Cosmin). Reduced dependency on C-runtime library when on Windows (Simon-Pierre) Replaced sprintf() with png_sprintf() (Simon-Pierre) version 1.4.0beta2 [April 20, 2006] Revised makefiles to avoid making links to libpng.so.* Moved some leftover MMX-related defines from pngconf.h to pngintrn.h Updated scripts/pngos2.def, pngw32.def, and projects/wince/png32ce.def Updated scripts/pngw32.def to comment out MMX functions. version 1.2.11beta1 [May 31, 2006] scripts/libpng.pc.in contained "configure" style version info and would not work with makefiles. The shared-library makefiles were linking to libpng.so.0 instead of libpng.so.3 compatibility as the library. version 1.4.0beta3 [May 10, 2006] Updated scripts/pngw32.def to comment out MMX functions. Added PNG_NO_GET_INT_32 and PNG_NO_SAVE_INT_32 macros. Revised pngconf.h and added pngconf.h.in so makefiles and configure can pass defines to libpng and applications. version 1.4.0beta4 [May 11, 2006] Revised configure.ac, Makefile.am, and many of the makefiles to write their defines in pngconf.h. version 1.4.0beta5 [May 15, 2006] Added a missing semicolon in Makefile.am and Makefile.in Deleted extraneous square brackets from configure.ac version 1.2.11beta2 [June 2, 2006] Increased sprintf buffer from 50 to 52 chars in pngrutil.c to avoid buffer overflow. Fixed bug in example.c (png_set_palette_rgb -> png_set_palette_to_rgb)) version 1.4.0beta6 [June 2, 2006] Changed sonum from 0 to 1. Removed unused prototype for png_check_sig() from png.h version 1.2.11beta3 [June 5, 2006] Prepended "#! /bin/sh" to ltmail.sh and contrib/pngminus/*.sh (Cosmin). Removed the accidental leftover Makefile.in~ (Cosmin). Avoided potential buffer overflow and optimized buffer in png_write_sCAL(), png_write_sCAL_s() (Cosmin). Removed the include directories and libraries from CFLAGS and LDFLAGS in scripts/makefile.gcc (Nelson A. de Oliveira, Cosmin). version 1.2.11beta4 [June 6, 2006] Allow zero-length IDAT chunks after the entire zlib datastream, but not after another intervening chunk type. version 1.2.11rc2 [June 14, 2006] Added prototypes for PNG_INCH_CONVERSIONS functions to png.h Revised INSTALL and autogen.sh Fixed typo in several makefiles (-W1 should be -Wl) version 1.2.11rc3 [June 15, 2006] Added one zero element to png_gamma_shift[] array in pngrtran.c to avoid reading out of bounds. version 1.4.0beta7 [June 16, 2006] Exported png_write_sig (Cosmin). Optimized buffer in png_handle_cHRM() (Cosmin). Set pHYs = 2835 x 2835 pixels per meter, and added sCAL = 0.352778e-3 x 0.352778e-3 meters, in pngtest.png (Cosmin). Added png_set_benign_errors(), png_benign_error(), png_chunk_benign_error(). Added typedef for png_int_32 and png_uint_32 on 64-bit systems. version 1.4.0beta8 [June 21, 2006] Added demonstration of user chunk support in pngtest.c, to support the public sTER chunk and a private vpAg chunk. version 1.4.0beta9 [July 3, 2006] Removed ordinals from scripts/pngw32.def and removed png_info_int and png_set_gray_1_2_4_to_8 entries. Inline call of png_get_uint_32() in png_get_uint_31(). Use png_get_uint_31() to get vpAg width and height in pngtest.c Removed WINCE and Netware projects. Removed standalone Y2KINFO file. version 1.4.0beta10 [July 12, 2006] Added "all: pngconf.h.in pngconf.h" target to Makefile.am version 1.4.0beta11 [August 19, 2006] Removed AC_FUNC_MALLOC from configure.ac. Added a warning when writing iCCP profile with mismatched profile length. Patched pnggccrd.c to assemble on x86_64 platforms. Moved chunk header reading into a separate function png_read_chunk_header() in pngrutil.c. The chunk header (len+sig) is now serialized in a single operation (Cosmin). Implemented support for I/O states. Added png_ptr member io_state, and functions png_get_io_chunk_name() and png_get_io_state() in pngget.c (Cosmin). Added png_get_io_chunk_name and png_get_io_state to scripts/*.def (Cosmin). Renamed scripts/pngw32.* to scripts/pngwin.* (Cosmin). Removed the include directories and libraries from CFLAGS and LDFLAGS in scripts/makefile.gcc (Cosmin). Used png_save_uint_32() to set vpAg width and height in pngtest.c (Cosmin). Cast to proper type when getting/setting vpAg units in pngtest.c (Cosmin). Added pngintrn.h to the Visual C++ projects (Cosmin). Removed scripts/list (Cosmin). Updated copyright year in scripts/pngwin.def (Cosmin). Removed PNG_TYPECAST_NULL and used standard NULL consistently (Cosmin). Disallowed the user to redefine png_size_t, and enforced a consistent use of png_size_t across libpng (Cosmin). Changed the type of png_ptr->rowbytes, PNG_ROWBYTES() and friends to png_size_t (Cosmin). Removed png_convert_size() and replaced png_sizeof with sizeof (Cosmin). Removed some unnecessary type casts (Cosmin). Changed prototype of png_get_compression_buffer_size() and png_set_compression_buffer_size() to work with png_size_t instead of png_uint_32 (Cosmin). Removed png_memcpy_check() and png_memset_check() (Cosmin). Fixed a typo (png_byte --> png_bytep) in libpng.3 and libpng.txt (Cosmin). Clarified that png_zalloc() does not clear the allocated memory, and png_zalloc() and png_zfree() cannot be PNGAPI (Cosmin). Renamed png_mem_size_t to png_alloc_size_t, fixed its definition in pngconf.h, and used it in all memory allocation functions (Cosmin). Renamed pngintrn.h to pngpriv.h, added a comment at the top of the file mentioning that the symbols declared in that file are private, and updated the scripts and the Visual C++ projects accordingly (Cosmin). Removed circular references between pngconf.h and pngconf.h.in in scripts/makefile.vc*win32 (Cosmin). Removing trailing '.' from the warning and error messages (Cosmin). Added pngdefs.h that is built by makefile or configure, instead of pngconf.h.in (Glenn). Detect and fix attempt to write wrong iCCP profile length. version 1.4.0beta12 [October 19, 2006] Changed "logical" to "bitwise" in the documentation. Work around Intel-Mac compiler bug by setting PNG_NO_MMX_CODE in pngconf.h Add a typecast to stifle compiler warning in pngrutil.c version 1.4.0beta13 [November 10, 2006] Fix potential buffer overflow in sPLT chunk handler. Fix Makefile.am to not try to link to noexistent files. version 1.4.0beta14 [November 15, 2006] Check all exported functions for NULL png_ptr. version 1.4.0beta15 [November 17, 2006] Relocated two misplaced tests for NULL png_ptr. Built Makefile.in with automake-1.9.6 instead of 1.9.2. Build configure with autoconf-2.60 instead of 2.59. Add "install: all" in Makefile.am so "configure; make install" will work. version 1.4.0beta16 [November 17, 2006] Added a typecast in png_zalloc(). version 1.4.0beta17 [December 4, 2006] Changed "new_key[79] = '\0';" to "(*new_key)[79] = '\0';" in pngwutil.c version 1.4.0beta18 [December 7, 2006] Added scripts/CMakeLists.txt version 1.4.0beta19 [May 16, 2007] Revised scripts/CMakeLists.txt Rebuilt configure and Makefile.in with newer tools. Added "png_ptr->num_trans=0" before error return in png_handle_tRNS, to eliminate a vulnerability (CVE-2007-2554, CERT VU#684664) version 1.4.0beta20 [July 9, 2008] Moved several PNG_HAVE_* macros from pngpriv.h to png.h because applications calling set_unknown_chunk_location() need them. Moved several macro definitions from pngpriv.h to pngconf.h Added png_ptr->unknown_chunk to hold working unknown chunk data, so it can be free'ed in case of error. Revised unknown chunk handling in pngrutil.c and pngpread.c to use this structure. Merge with changes to the 1.2.X branch, as of 1.2.19beta10. Revised makefile.mingw Prefer PNG_USE_PNGVCRD when _MSC_VER is defined in pngconf.h version 1.4.0beta21 [July 21, 2008] Moved local array "chunkdata" from pngrutil.c to the png_struct, so it will be freed by png_read_destroy() in case of a read error (Kurt Christensen). version 1.4.0beta22 [July 21, 2008] Change "purpose" and "buffer" to png_ptr->chunkdata to avoid memory leaking. version 1.4.0beta23 [July 22, 2008] Change "chunkdata = NULL" to "png_ptr->chunkdata = NULL" several places in png_decompress_chunk(). version 1.4.0beta24 [July 25, 2008] Change all remaining "chunkdata" to "png_ptr->chunkdata" in png_decompress_chunk(), and remove "chunkdata" from parameter list. Put a call to png_check_chunk_name() in png_read_chunk_header(). Revised png_check_chunk_name() to reject a name with a lowercase 3rd byte. Removed two calls to png_check_chunk_name() occuring later in the process. Define PNG_NO_ERROR_NUMBERS by default in pngconf.h version 1.4.0beta25 [July 30, 2008] Added a call to png_check_chunk_name() in pngpread.c Reverted png_check_chunk_name() to accept a name with a lowercase 3rd byte. Added png_push_have_buffer() function to pngpread.c Eliminated PNG_BIG_ENDIAN_SUPPORTED and associated png_get_* macros. Made inline expansion of png_get_*() optional with PNG_USE_READ_MACROS. Eliminated all PNG_USELESS_TESTS and PNG_CORRECT_PALETTE_SUPPORTED code. Synced contrib directory and configure files with libpng-1.2.30beta06. Eliminated no-longer-used pngdefs.h (but it's still built in the makefiles) Relocated a misplaced "#endif /* PNG_NO_WRITE_FILTER */" in pngwutil.c version 1.4.0beta26 [August 4, 2008] Removed png_push_have_buffer() function in pngpread.c. It increased the compiled library size slightly. Changed "-Wall" to "-W -Wall" in the CFLAGS in all makefiles (Cosmin Truta) Declared png_ptr "volatile" in pngread.c and pngwrite.c to avoid warnings. Updated contrib/visupng/cexcept.h to version 2.0.1 Added PNG_LITERAL_CHARACTER macros for #, [, and ]. version 1.4.0beta27 [August 5, 2008] Revised usage of PNG_LITERAL_SHARP in pngerror.c. Moved newline character from individual png_debug messages into the png_debug macros. Allow user to #define their own png_debug, png_debug1, and png_debug2. version 1.4.0beta28 [August 5, 2008] Revised usage of PNG_LITERAL_SHARP in pngerror.c. Added PNG_STRING_NEWLINE macro version 1.4.0beta29 [August 9, 2008] Revised usage of PNG_STRING_NEWLINE to work on non-ISO compilers. Added PNG_STRING_COPYRIGHT macro. Added non-ISO versions of png_debug macros. version 1.4.0beta30 [August 14, 2008] Added premultiplied alpha feature (Volker Wiendl). version 1.4.0beta31 [August 18, 2008] Moved png_set_premultiply_alpha from pngtrans.c to pngrtran.c Removed extra crc check at the end of png_handle_cHRM(). Bug introduced in libpng-1.4.0beta20. version 1.4.0beta32 [August 19, 2008] Added PNG_WRITE_FLUSH_SUPPORTED block around new png_flush() call. Revised PNG_NO_STDIO version of png_write_flush() version 1.4.0beta33 [August 20, 2008] Added png_set_chunk_cache_max() to limit the total number of sPLT, text, and unknown chunks that can be stored. version 1.4.0beta34 [September 6, 2008] Shortened tIME_string to 29 bytes in pngtest.c Fixed off-by-one error introduced in png_push_read_zTXt() function in libpng-1.2.30beta04/pngpread.c (Harald van Dijk) version 1.4.0beta35 [October 6, 2008] Changed "trans_values" to "trans_color". Change png_set_gray_1_2_4_to_8() to png_set_expand_gray_1_2_4_to_8() in example.c (debian bug report) version 1.4.0beta36 [October 25, 2008] Sync with tEXt vulnerability fix in libpng-1.2.33rc02. version 1.4.0beta37 [November 13, 2008] Added png_check_cHRM in png.c and moved checking from pngget.c, pngrutil.c, and pngwrite.c version 1.4.0beta38 [November 22, 2008] Added check for zero-area RGB cHRM triange in png_check_cHRM() and png_check_cHRM_fixed(). version 1.4.0beta39 [November 23, 2008] Revised png_warning() to write its message on standard output by default when warning_fn is NULL. version 1.4.0beta40 [November 24, 2008] Eliminated png_check_cHRM(). Instead, always use png_check_cHRM_fixed(). In png_check_cHRM_fixed(), ensure white_y is > 0, and removed redundant check for all-zero coordinates that is detected by the triangle check. version 1.4.0beta41 [November 26, 2008] Fixed string vs pointer-to-string error in png_check_keyword(). Rearranged test expressions in png_check_cHRM_fixed() to avoid internal overflows. Added PNG_NO_CHECK_cHRM conditional. version 1.4.0beta42, 43 [December 1, 2008] Merge png_debug with version 1.2.34beta04. version 1.4.0beta44 [December 6, 2008] Removed redundant check for key==NULL before calling png_check_keyword() to ensure that new_key gets initialized and removed extra warning (Merge with version 1.2.34beta05 -- Arvan Pritchard). version 1.4.0beta45 [December 9, 2008] In png_write_png(), respect the placement of the filler bytes in an earlier call to png_set_filler() (Jim Barry). version 1.4.0beta46 [December 10, 2008] Undid previous change and added PNG_TRANSFORM_STRIP_FILLER_BEFORE and PNG_TRANSFORM_STRIP_FILLER_AFTER conditionals and deprecated PNG_TRANSFORM_STRIP_FILLER (Jim Barry). version 1.4.0beta47 [December 15, 2008] Turned off PNG_READ_DITHER_SUPPORTED by default. version 1.4.0beta48 [February 14, 2009] Added new exported function png_calloc(). Combined several instances of png_malloc(); png_memset() into png_calloc(). Removed prototype for png_freeptr() that was added in libpng-1.4.0beta24 version 1.4.0beta49 [February 28, 2009] Added png_fileno() macro to pngconf.h, used in pngwio.c Corrected order of #ifdef's in png_debug definition in png.h Fixed bug introduced in libpng-1.4.0beta48 with the memset arguments for pcal_params. Fixed order of #ifdef directives in the png_debug defines in png.h (bug introduced in libpng-1.2.34/1.4.0beta29). Revised comments in png_set_read_fn() and png_set_write_fn(). version 1.4.0beta50 [March 18, 2009] Use png_calloc() instead of png_malloc() to allocate big_row_buf when reading an interlaced file, to avoid a possible UMR. Undid recent revision of PNG_NO_STDIO version of png_write_flush(). Users having trouble with fflush() can build with PNG_NO_WRITE_FLUSH defined or supply their own flush_fn() replacement. Revised libpng*.txt and png.h documentation about use of png_write_flush() and png_set_write_fn(). Removed fflush() from pngtest.c. Added "#define PNG_NO_WRITE_FLUSH" to contrib/pngminim/encoder/pngusr.h version 1.4.0beta51 [March 21, 2009] Removed new png_fileno() macro from pngconf.h . version 1.4.0beta52 [March 27, 2009] Relocated png_do_chop() ahead of building gamma tables in pngrtran.c This avoids building 16-bit gamma tables unnecessarily. Removed fflush() from pngtest.c. Added "#define PNG_NO_WRITE_FLUSH" to contrib/pngminim/encoder/pngusr.h Added a section on differences between 1.0.x and 1.2.x to libpng.3/libpng.txt version 1.4.0beta53 [April 1, 2009] Removed some remaining MMX macros from pngpriv.h Fixed potential memory leak of "new_name" in png_write_iCCP() (Ralph Giles) version 1.4.0beta54 [April 13, 2009] Added "ifndef PNG_SKIP_SETJMP_CHECK" block in pngconf.h to allow application code writers to bypass the check for multiple inclusion of setjmp.h when they know that it is safe to ignore the situation. Eliminated internal use of setjmp() in pngread.c and pngwrite.c Reordered ancillary chunks in pngtest.png to be the same as what pngtest now produces, and made some cosmetic changes to pngtest output. Eliminated deprecated png_read_init_3() and png_write_init_3() functions. version 1.4.0beta55 [April 15, 2009] Simplified error handling in pngread.c and pngwrite.c by putting the new png_read_cleanup() and png_write_cleanup() functions inline. version 1.4.0beta56 [April 25, 2009] Renamed "user_chunk_data" to "my_user_chunk_data" in pngtest.c to suppress "shadowed declaration" warning from gcc-4.3.3. Renamed "gamma" to "png_gamma" in pngset.c to avoid "shadowed declaration" warning about a global "gamma" variable in math.h on some platforms. version 1.4.0beta57 [May 2, 2009] Removed prototype for png_freeptr() that was added in libpng-1.4.0beta24 but was never defined (again). Rebuilt configure scripts with autoconf-2.63 instead of 2.62 Removed pngprefs.h and MMX from makefiles version 1.4.0beta58 [May 14, 2009] Changed pngw32.def to pngwin.def in makefile.mingw (typo was intruduced in beta57). Clarified usage of sig_bit versus sig_bit_p in example.c (Vincent Torri) version 1.4.0beta59 [May 15, 2009] Reformated sources in libpng style (3-space intentation, comment format) Fixed typo in libpng docs (PNG_FILTER_AVE should be PNG_FILTER_AVG) Added sections about the git repository and our coding style to the documentation Relocated misplaced #endif in pngwrite.c, sCAL chunk handler. version 1.4.0beta60 [May 19, 2009] Conditionally compile png_read_finish_row() which is not used by progressive readers. Added contrib/pngminim/preader to demonstrate building minimal progressive decoder, based on contrib/gregbook with embedded libpng and zlib. version 1.4.0beta61 [May 20, 2009] In contrib/pngminim/*, renamed "makefile.std" to "makefile", since there is only one makefile in those directories, and revised the README files accordingly. More reformatting of comments, mostly to capitalize sentences. version 1.4.0beta62 [June 2, 2009] Added "#define PNG_NO_WRITE_SWAP" to contrib/pngminim/encoder/pngusr.h and "define PNG_NO_READ_SWAP" to decoder/pngusr.h and preader/pngusr.h Reformatted several remaining "else statement" into two lines. Added a section to the libpng documentation about using png_get_io_ptr() in configure scripts to detect the presence of libpng. version 1.4.0beta63 [June 15, 2009] Revised libpng*.txt and libpng.3 to mention calling png_set_IHDR() multiple times and to specify the sample order in the tRNS chunk, because the ISO PNG specification has a typo in the tRNS table. Changed several PNG_UNKNOWN_CHUNK_SUPPORTED to PNG_HANDLE_AS_UNKNOWN_SUPPORTED, to make the png_set_keep mechanism available for ignoring known chunks even when not saving unknown chunks. Adopted preference for consistent use of "#ifdef" and "#ifndef" versus "#if defined()" and "if !defined()" where possible. version 1.4.0beta64 [June 24, 2009] Eliminated PNG_LEGACY_SUPPORTED code. Moved the various unknown chunk macro definitions outside of the PNG_READ|WRITE_ANCILLARY_CHUNK_SUPPORTED blocks. version 1.4.0beta65 [June 26, 2009] Added a reference to the libpng license in each file. version 1.4.0beta66 [June 27, 2009] Refer to the libpng license instead of the libpng license in each file. version 1.4.0beta67 [July 6, 2009] Relocated INVERT_ALPHA within png_read_png() and png_write_png(). Added high-level API transform PNG_TRANSFORM_GRAY_TO_RGB. Added an "xcode" project to the projects directory (Alam Arias). version 1.4.0beta68 [July 19, 2009] Avoid some tests in filter selection in pngwutil.c version 1.4.0beta69 [July 25, 2009] Simplified the new filter-selection test. This runs faster in the common "PNG_ALL_FILTERS" and PNG_FILTER_NONE cases. Removed extraneous declaration from the new call to png_read_gray_to_rgb() (bug introduced in libpng-1.4.0beta67). Fixed up xcode project (Alam Arias) version 1.4.0beta70 [July 27, 2009] Avoid a possible NULL dereference in debug build, in png_set_text_2(). (bug introduced in libpng-0.95, discovered by Evan Rouault) version 1.4.0beta71 [July 29, 2009] Rebuilt configure scripts with autoconf-2.64. Added a prototype for png_64bit_product() in png.c version 1.4.0beta72 [August 1, 2009] Replaced *.tar.lzma with *.tar.xz in distribution. Get the xz codec from . version 1.4.0beta73 [August 1, 2009] Reject attempt to write iCCP chunk with negative embedded profile length (JD Chen) version 1.4.0beta74 [August 8, 2009] Changed png_ptr and info_ptr member "trans" to "trans_alpha". version 1.4.0beta75 [August 21, 2009] Removed an extra png_debug() recently added to png_write_find_filter(). Fixed incorrect #ifdef in pngset.c regarding unknown chunk support. version 1.4.0beta76 [August 21, 2009] version 1.4.0betaN [future] Build shared libraries with -lz and sometimes -lm. Send comments/corrections/commendations to png-mng-implement at lists.sf.net (subscription required; visit https://lists.sourceforge.net/lists/listinfo/png-mng-implement to subscribe) or to glennrp at users.sourceforge.net Glenn R-P