1*8ae6144bSmsaitoh.\" $NetBSD: elf.5,v 1.16 2024/05/13 00:01:53 msaitoh Exp $ 26ce5077cSpooka.\" 35eb3bf91Sthorpej.\" Copyright (c) 2001, 2002 The NetBSD Foundation, Inc. 46ce5077cSpooka.\" All rights reserved. 56ce5077cSpooka.\" 66ce5077cSpooka.\" This document is derived from work contributed to The NetBSD Foundation 75eb3bf91Sthorpej.\" by Antti Kantee. 86ce5077cSpooka.\" 96ce5077cSpooka.\" Redistribution and use in source and binary forms, with or without 106ce5077cSpooka.\" modification, are permitted provided that the following conditions 116ce5077cSpooka.\" are met: 126ce5077cSpooka.\" 1. Redistributions of source code must retain the above copyright 136ce5077cSpooka.\" notice, this list of conditions and the following disclaimer. 146ce5077cSpooka.\" 2. Redistributions in binary form must reproduce the above copyright 156ce5077cSpooka.\" notice, this list of conditions and the following disclaimer in the 166ce5077cSpooka.\" documentation and/or other materials provided with the distribution. 176ce5077cSpooka.\" 186ce5077cSpooka.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS 196ce5077cSpooka.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 206ce5077cSpooka.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 216ce5077cSpooka.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE 226ce5077cSpooka.\" LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 236ce5077cSpooka.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 246ce5077cSpooka.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 256ce5077cSpooka.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 266ce5077cSpooka.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 276ce5077cSpooka.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 286ce5077cSpooka.\" POSSIBILITY OF SUCH DAMAGE. 296ce5077cSpooka.\" 30e518d424Spooka.Dd November 18, 2006 316ce5077cSpooka.Dt ELF 5 326ce5077cSpooka.Os 336ce5077cSpooka.Sh NAME 346ce5077cSpooka.Nm ELF 356ce5077cSpooka.Nd executable and linking format 366ce5077cSpooka.Sh SYNOPSIS 37472351e1Swiz.In elf.h 386ce5077cSpooka.Sh DESCRIPTION 396ce5077cSpookaBecause of the flexible nature of ELF, the structures describing it are 406ce5077cSpookaavailable both as 32bit and 64bit versions. This document uses the 32bit 416ce5077cSpookaversions, refer to 425e015e5eSjoerg.In elf.h 436ce5077cSpookafor the corresponding 64bit versions. 446ce5077cSpooka.Pp 455eb3bf91SthorpejThe four main types of an ELF object file are: 466ce5077cSpooka.Bl -tag -width "relocatable" 476ce5077cSpooka.It executable 486ce5077cSpookaA file suitable for execution. It contains the information required for 496ce5077cSpookacreating a new process image. 506ce5077cSpooka.It relocatable 516ce5077cSpookaContains the necessary information to be run through the link editor 526ce5077cSpooka.Xr ld 1 536ce5077cSpookato create an executable or a shared library. 546ce5077cSpooka.It shared 556ce5077cSpookaThe shared object contains necessary information which can be used by 566ce5077cSpookaeither the link editor 576ce5077cSpooka.Xr ld 1 586ce5077cSpookaat link time or by the dynamic loader 59deaad9bdSpooka.Xr ld.elf_so 1 606ce5077cSpookaat run time. 615eb3bf91Sthorpej.It core 625eb3bf91SthorpejA file which describes the virtual address space and register state 635eb3bf91Sthorpejof a process. Core files are typically used in conjunction with 645eb3bf91Sthorpejdebuggers such as 655eb3bf91Sthorpej.Xr gdb 1 . 666ce5077cSpooka.El 676ce5077cSpooka.Pp 68deaad9bdSpookaELF files have a dual nature. The toolchain, including tools such as the 696ce5077cSpooka.Xr as 1 706ce5077cSpookaand linker 71deaad9bdSpooka.Xr ld 1 , 72deaad9bdSpookatreats them as a set of sections described by their section headers. The system 736ce5077cSpookaloader treats them as a set of segments described by the program headers. 746ce5077cSpooka.Pp 756ce5077cSpookaThe general format of an ELF file is the following: The file starts with an 766ce5077cSpookaELF header. This is followed by a table of program headers (optional for 77deaad9bdSpookarelocatable and shared files). After this come the sections/segments. 786ce5077cSpookaThe file ends with a table of section headers (optional for executable 796ce5077cSpookafiles). 806ce5077cSpooka.Pp 81deaad9bdSpookaA segment can be considered to consist of several sections. For example, 82deaad9bdSpookaall executable sections are typically packed into one loadable segment 83deaad9bdSpookawhich is read-only and executable (see 84deaad9bdSpooka.Fa p_flags 85deaad9bdSpookain the program header). This enables the system to map the entire file with 86deaad9bdSpookajust a few operations, one for each loadable segment, instead of doing 87deaad9bdSpookanumerous map operations for each section separately. 886ce5077cSpooka.Pp 896ce5077cSpookaEach file is described by the ELF header: 906ce5077cSpooka.Bd -literal -offset indent 916ce5077cSpookatypedef struct { 926ce5077cSpooka unsigned char e_ident[ELF_NIDENT]; 936ce5077cSpooka Elf32_Half e_type; 946ce5077cSpooka Elf32_Half e_machine; 956ce5077cSpooka Elf32_Word e_version; 966ce5077cSpooka Elf32_Addr e_entry; 976ce5077cSpooka Elf32_Off e_phoff; 986ce5077cSpooka Elf32_Off e_shoff; 996ce5077cSpooka Elf32_Word e_flags; 1006ce5077cSpooka Elf32_Half e_ehsize; 1016ce5077cSpooka Elf32_Half e_phentsize; 1026ce5077cSpooka Elf32_Half e_phnum; 1036ce5077cSpooka Elf32_Half e_shentsize; 1046ce5077cSpooka Elf32_Half e_shnum; 1056ce5077cSpooka Elf32_Half e_shstrndx; 1066ce5077cSpooka} Elf32_Ehdr; 1076ce5077cSpooka.Ed 1086ce5077cSpooka.Pp 1096ce5077cSpooka.Bl -tag -width "e_phentsize" 1106ce5077cSpooka.It Fa e_ident[] 1116ce5077cSpookaThe array contains the following information in the indicated locations: 1126ce5077cSpooka.Bl -tag -width EI_ABIVERSION 1132cfd4db5Spooka.It Dv EI_MAG0 1146ce5077cSpookaThe elements ranging from 1152cfd4db5Spooka.Dv EI_MAG0 1166ce5077cSpookato 1172cfd4db5Spooka.Dv EI_MAG3 1186ce5077cSpookacontain the ELF magic number: \\0177ELF 1196ce5077cSpooka.It Dv EI_CLASS 1206ce5077cSpookaContains the address size of the binary, either 32 or 64bit. 1216ce5077cSpooka.It Dv EI_DATA 1226ce5077cSpookabyte order 1236ce5077cSpooka.It Dv EI_VERSION 1246ce5077cSpookaContains the ELF header version. This is currently always set to 1. 1256ce5077cSpooka.It Dv EI_OSABI 126deaad9bdSpookaContains the operating system ABI identification. Note that even though the 127deaad9bdSpookadefinition 128deaad9bdSpooka.Dv ELFOSABI_NETBSD 129deaad9bdSpookaexists, 130deaad9bdSpooka.Nx 131deaad9bdSpookauses 132deaad9bdSpooka.Dv ELFOSABI_SYSV 133deaad9bdSpookahere, since the 134deaad9bdSpooka.Nx 135deaad9bdSpookaABI does not deviate from the standard. 1366ce5077cSpooka.It Dv EI_ABIVERSION 1376ce5077cSpookaABI version. 1386ce5077cSpooka.El 1396ce5077cSpooka.It Fa e_type 1406ce5077cSpookaContains the file type identification. It can be either 1416ce5077cSpooka.Dv ET_REL , 1426ce5077cSpooka.Dv ET_EXEC , 1436ce5077cSpooka.Dv ET_DYN , 1446ce5077cSpookaor 1456ce5077cSpooka.Dv ET_CORE 1466ce5077cSpookafor relocatable, executable, shared, or core, respectively. 1476ce5077cSpooka.It Fa e_machine 1486ce5077cSpookaContains the machine type, e.g. SPARC, Alpha, MIPS, ... 1496ce5077cSpooka.It Fa e_entry 1506ce5077cSpookaThe program entry point if the file is executable. 1516ce5077cSpooka.It Fa e_phoff 1526ce5077cSpookaThe position of the program header table in the file or 0 if it doesn't exist. 1536ce5077cSpooka.It Fa e_shoff 1546ce5077cSpookaThe position of the section header table in the file or 0 if it doesn't exist. 1556ce5077cSpooka.It Fa e_flags 156deaad9bdSpookaContains processor-specific flags. For example, the SPARC port uses this 157deaad9bdSpookaspace to specify what kind of memory store ordering is required. 1586ce5077cSpooka.It Fa e_ehsize 1596ce5077cSpookaThe size of the ELF header. 1606ce5077cSpooka.It Fa e_phentsize 161deaad9bdSpookaThe size of an entry in the program header table. All entries are the same 162deaad9bdSpookasize. 1636ce5077cSpooka.It Fa e_phnum 1646ce5077cSpookaThe number of entries in the program header table, or 0 if none exists. 1656ce5077cSpooka.It Fa e_shentsize 166deaad9bdSpookaThe size of an entry in the section header table. All entries are the same 167deaad9bdSpookasize. 1686ce5077cSpooka.It Fa e_shnum 1696ce5077cSpookaThe number of entries in the section header table, or 0 if none exists. 1706ce5077cSpooka.It Fa e_shstrndx 1716ce5077cSpookaContains the index number of the section which contains the section 1726ce5077cSpookaname strings. 1736ce5077cSpooka.El 1746ce5077cSpooka.Pp 1756ce5077cSpookaEach ELF section in turn is described by the section header: 1766ce5077cSpooka.Bd -literal -offset indent 1776ce5077cSpookatypedef struct { 1786ce5077cSpooka Elf32_Word sh_name; 1796ce5077cSpooka Elf32_Word sh_type; 1806ce5077cSpooka Elf32_Word sh_flags; 1816ce5077cSpooka Elf32_Addr sh_addr; 1826ce5077cSpooka Elf32_Off sh_offset; 1836ce5077cSpooka Elf32_Word sh_size; 1846ce5077cSpooka Elf32_Word sh_link; 1856ce5077cSpooka Elf32_Word sh_info; 1866ce5077cSpooka Elf32_Word sh_addralign; 1876ce5077cSpooka Elf32_Word sh_entsize; 1886ce5077cSpooka} Elf32_Shdr; 1896ce5077cSpooka.Ed 1906ce5077cSpooka.Pp 1916ce5077cSpooka.Bl -tag -width "sh_addralign" 1926ce5077cSpooka.It Fa sh_name 1936ce5077cSpookaContains an index to the position in the section header string section where 1946ce5077cSpookathe name of the current section can be found. 1956ce5077cSpooka.It Fa sh_type 1966ce5077cSpookaContains the section type indicator. The more important possible values are: 1976ce5077cSpooka.Bl -tag -width "SHT_PROGBITS" 1986ce5077cSpooka.It Dv SHT_NULL 1996ce5077cSpookaSection is inactive. The other fields contain undefined values. 2006ce5077cSpooka.It Dv SHT_PROGBITS 2016ce5077cSpookaSection contains program information. It can be for example code, data, 2026ce5077cSpookaor debugger information. 2036ce5077cSpooka.It Dv SHT_SYMTAB 2046ce5077cSpookaSection contains a symbol table. This section usually contains all the 2056ce5077cSpookasymbols and is intended for the regular link editor 2066ce5077cSpooka.Xr ld 1 . 2076ce5077cSpooka.It Dv SHT_STRTAB 2086ce5077cSpookaSection contains a string table. 2096ce5077cSpooka.It Dv SHT_RELA 210deaad9bdSpookaSection contains relocation information with an explicit addend. 2116ce5077cSpooka.It Dv SHT_HASH 2126ce5077cSpookaSection contains a symbol hash table. 2136ce5077cSpooka.It Dv SHT_DYNAMIC 2146ce5077cSpookaSection contains dynamic linking information. 2156ce5077cSpooka.It Dv SHT_NOTE 2166ce5077cSpookaSection contains some special information. The format can be e.g. 2176ce5077cSpookavendor-specific. 2186ce5077cSpooka.It Dv SHT_NOBITS 2196ce5077cSpookaSections contains information similar to 2206ce5077cSpooka.Dv SHT_PROGBITS , 2216ce5077cSpookabut takes up no space in the file. This can be used for e.g. bss. 2226ce5077cSpooka.It Dv SHT_REL 223deaad9bdSpookaSection contains relocation information without an explicit addend. 2246ce5077cSpooka.It Dv SHT_SHLIB 2256ce5077cSpookaThis section type is reserved but has unspecified semantics. 2266ce5077cSpooka.It Dv SHT_DYNSYM 2276ce5077cSpookaSection contains a symbol table. This symbol table is intended for the 2286ce5077cSpookadynamic linker, and is kept as small as possible to conserve space, since 2296ce5077cSpookait must be loaded to memory at run time. 2306ce5077cSpooka.El 2316ce5077cSpooka.It Fa sh_flags 2326ce5077cSpookaContains the section flags, which can have the following values or any 2336ce5077cSpookacombination of them: 2346ce5077cSpooka.Bl -tag -width SHF_EXECINSTR 2356ce5077cSpooka.It Dv SHF_WRITE 2366ce5077cSpookaSection is writable after it has been loaded. 2376ce5077cSpooka.It Dv SHF_ALLOC 2386ce5077cSpookaSection will occupy memory at run time. 2396ce5077cSpooka.It Dv SHF_EXECINSTR 2406ce5077cSpookaSection contains executable machine instructions. 2416ce5077cSpooka.El 2426ce5077cSpooka.It Fa sh_addr 2436ce5077cSpookaAddress to where the section will be loaded, or 0 if this section does not 2446ce5077cSpookareside in memory at run time. 2456ce5077cSpooka.It Fa sh_offset 2466ce5077cSpookaThe byte offset from the beginning of the file to the beginning of this 2476ce5077cSpookasection. If the section is of type 2486ce5077cSpooka.Dv SHT_NOBITS , 2496ce5077cSpookathis field specifies the conceptual placement in the file. 2506ce5077cSpooka.It Fa sh_size 2516ce5077cSpookaThe size of the section in the file for all types except 2526ce5077cSpooka.Dv SHT_NOBITS . 2536ce5077cSpookaFor that type the value may differ from zero, but the section will still 2546ce5077cSpookaalways take up no space from the file. 2556ce5077cSpooka.It Fa sh_link 2566ce5077cSpookaContains an index to the section header table. The interpretation depends 2576ce5077cSpookaon the section type as follows: 2586ce5077cSpooka.Pp 2596ce5077cSpooka.Bl -tag -compact -width SHT_DYNAMIC 2606ce5077cSpooka.It Dv SHT_REL 2616ce5077cSpooka.It Dv SHT_RELA 2626ce5077cSpookaSection index of the associated symbol table. 2636ce5077cSpooka.Pp 2646ce5077cSpooka.It Dv SHT_SYMTAB 2656ce5077cSpooka.It Dv SHT_DYNSYM 2666ce5077cSpookaSection index of the associated string table. 2676ce5077cSpooka.Pp 2686ce5077cSpooka.It Dv SHT_HASH 2696ce5077cSpookaSection index of the symbol table to which the hash table applies. 2706ce5077cSpooka.Pp 2716ce5077cSpooka.It Dv SHT_DYNAMIC 272*8ae6144bSmsaitohSection index of the string table by which entries in this section are used. 2736ce5077cSpooka.El 2746ce5077cSpooka.It Fa sh_info 2756ce5077cSpookaContains extra information. The interpretation depends on the type as 2766ce5077cSpookafollows: 2776ce5077cSpooka.Pp 2786ce5077cSpooka.Bl -tag -compact -width SHT_DYNSYM 2796ce5077cSpooka.It Dv SHT_REL 2806ce5077cSpooka.It Dv SHT_RELA 2816ce5077cSpookaSection index of the section to which the relocation information applies. 2826ce5077cSpooka.Pp 2836ce5077cSpooka.It Dv SHT_SYMTAB 2846ce5077cSpooka.It Dv SHT_DYNSYM 2856ce5077cSpookaContains a value one greater that the last local symbol table index. 2866ce5077cSpooka.El 2876ce5077cSpooka.It Fa sh_addralign 2886ce5077cSpookaMarks the section alignment requirement. If, for example, the section contains 2896ce5077cSpookaa doubleword, the entire section must be doubleword aligned to ensure proper 2906ce5077cSpookaalignment. Only 0 and integral powers of two are allowed. Values 0 and 1 2916ce5077cSpookadenote that the section has no alignment. 2926ce5077cSpooka.It Fa sh_entsize 2938a940b23SuebayasiContains the entry size of an element for sections which are constructed 2946ce5077cSpookaof a table of fixed-size entries. If the section does not hold a table of 2956ce5077cSpookafixed-size entries, this value is 0. 2966ce5077cSpooka.El 2976ce5077cSpooka.Pp 2986ce5077cSpookaEvery executable object must contain a program header. The program header 2996ce5077cSpookacontains information necessary in constructing a process image. 3006ce5077cSpooka.Bd -literal -offset indent 3016ce5077cSpookatypedef struct { 3026ce5077cSpooka Elf32_Word p_type; 3036ce5077cSpooka Elf32_Off p_offset; 3046ce5077cSpooka Elf32_Addr p_vaddr; 3056ce5077cSpooka Elf32_Addr p_paddr; 3066ce5077cSpooka Elf32_Word p_filesz; 3076ce5077cSpooka Elf32_Word p_memsz; 3086ce5077cSpooka Elf32_Word p_flags; 3096ce5077cSpooka Elf32_Word p_align; 3106ce5077cSpooka} Elf32_Phdr; 3116ce5077cSpooka.Ed 3126ce5077cSpooka.Pp 3136ce5077cSpooka.Bl -tag -width p_offset 3146ce5077cSpooka.It Fa p_type 3156ce5077cSpookaContains the segment type indicator. The possible values are: 3166ce5077cSpooka.Bl -tag -width PT_DYNAMIC 3176ce5077cSpooka.It Dv PT_NULL 3186ce5077cSpookaSegment is inactive. The other fields contain undefined values. 3196ce5077cSpooka.It Dv PT_LOAD 3206ce5077cSpookaSegment is loadable. It is loaded to the address described by 3216ce5077cSpooka.Fa p_vaddr . 3226ce5077cSpookaIf 3236ce5077cSpooka.Fa p_memsz 3246ce5077cSpookais greater than 3256ce5077cSpooka.Fa p_filesz , 3266ce5077cSpookathe memory range from 3276ce5077cSpooka.Po Fa p_vaddr 3286ce5077cSpooka+ 3296ce5077cSpooka.Fa p_filesz Pc 3306ce5077cSpookato 3316ce5077cSpooka.Po Fa p_vaddr 3326ce5077cSpooka+ 3336ce5077cSpooka.Fa p_memsz Pc 3346ce5077cSpookais zero-filled when the segment is loaded. 3356ce5077cSpooka.Fa p_filesz 3366ce5077cSpookacan not be greater than 3376ce5077cSpooka.Fa p_memsz . 3386ce5077cSpookaSegments of this type are sorted in the header table by 3396ce5077cSpooka.Fa p_vaddr 3406ce5077cSpookain ascending order. 3416ce5077cSpooka.It Dv PT_DYNAMIC 3426ce5077cSpookaSegment contains dynamic linking information. 3436ce5077cSpooka.It Dv PT_INTERP 3446ce5077cSpookaSegment contains a null-terminated path name to the interpreter. This segment 3456ce5077cSpookamay be present only once in a file, and it must appear before any loadable 346deaad9bdSpookasegments. This field will most likely contain the ELF dynamic loader: 347e518d424Spooka.Pa /libexec/ld.elf_so 3486ce5077cSpooka.It Dv PT_NOTE 3496ce5077cSpookaSegment contains some special information. Format can be e.g. vendor-specific. 3506ce5077cSpooka.It Dv PT_SHLIB 3516ce5077cSpookaThis segment type is reserved but has unspecified semantics. Programs 352deaad9bdSpookawhich contain a segment of this type do not conform to the ABI, and must 353deaad9bdSpookaindicate this by setting the appropriate ABI in the ELF header 354deaad9bdSpooka.Dv EI_OSABI 355deaad9bdSpookafield. 3566ce5077cSpooka.It Dv PT_PHDR 357deaad9bdSpookaThe values in a program header of this type specify the characteristics 358deaad9bdSpookaof the program header table itself. For example, the 359deaad9bdSpooka.Fa p_vaddr 360deaad9bdSpookafield specifies the program header table location in memory once the 361deaad9bdSpookaprogram is loaded. This field may not occur more than once, may occur only 362deaad9bdSpookaif the program header table is part of the file memory image, and must 363deaad9bdSpookacome before any loadable segments. 3646ce5077cSpooka.El 3656ce5077cSpooka.It Fa p_offset 3666ce5077cSpookaContains the byte offset from the beginning of the file to the beginning 3676ce5077cSpookaof this segment. 3686ce5077cSpooka.It Fa p_vaddr 3696ce5077cSpookaContains the virtual memory address to which this segment is loaded. 3706ce5077cSpooka.It Fa p_paddr 371deaad9bdSpookaContains the physical address to which this segment is loaded. This value 372deaad9bdSpookais usually ignored, but may be used while bootstrapping or in embedded 373deaad9bdSpookasystems. 3746ce5077cSpooka.It Fa p_filesz 3756ce5077cSpookaContains the number of bytes this segment occupies in the file image. 3766ce5077cSpooka.It Fa p_memsz 3776ce5077cSpookaContains the number of bytes this segment occupies in the memory image. 3786ce5077cSpooka.It Fa p_flags 3796ce5077cSpookaContains the segment flags, which specify the permissions for the segment 3806ce5077cSpookaafter it has been loaded. The following values or any combination of them 3816ce5077cSpookais acceptable: 3826ce5077cSpooka.Bl -tag -width PF_R 3836ce5077cSpooka.It Dv PF_R 3846ce5077cSpookaSegment can be read. 385542ed9c1Swiz.It Dv PF_W 3866ce5077cSpookaSegment can be written. 3876ce5077cSpooka.It Dv PF_X 3886ce5077cSpookaSegment is executable. 3896ce5077cSpooka.El 3906ce5077cSpooka.It Fa p_align 3916ce5077cSpookaContains the segment alignment. Acceptable values are 0 and 1 for no alignment, 3926ce5077cSpookaand integral powers of two. 3936ce5077cSpooka.Fa p_vaddr 3946ce5077cSpookashould equal 3956ce5077cSpooka.Fa p_offset 3966ce5077cSpookamodulo 3976ce5077cSpooka.Fa p_align . 3986ce5077cSpooka.El 3996ce5077cSpooka.Sh SEE ALSO 4006ce5077cSpooka.Xr as 1 , 4016ce5077cSpooka.Xr gdb 1 , 4026ce5077cSpooka.Xr ld 1 , 403deaad9bdSpooka.Xr ld.elf_so 1 , 4046ce5077cSpooka.Xr execve 2 , 4056ce5077cSpooka.Xr nlist 3 , 4066ce5077cSpooka.Xr a.out 5 , 40742704c41Swiz.Xr core 5 , 4086ce5077cSpooka.Xr link 5 , 40942704c41Swiz.Xr stab 5 4106ce5077cSpooka.Sh HISTORY 4115eb3bf91SthorpejThe ELF object file format first appeared in 4126ce5077cSpooka.At V . 413