This is libc.info, produced by makeinfo version 4.8 from libc.texinfo.

INFO-DIR-SECTION GNU libraries
START-INFO-DIR-ENTRY
* Libc: (libc).                 C library.
END-INFO-DIR-ENTRY

INFO-DIR-SECTION GNU C library functions and macros
START-INFO-DIR-ENTRY
* ALTWERASE: (libc)Local Modes.
* ARGP_ERR_UNKNOWN: (libc)Argp Parser Functions.
* ARG_MAX: (libc)General Limits.
* BC_BASE_MAX: (libc)Utility Limits.
* BC_DIM_MAX: (libc)Utility Limits.
* BC_SCALE_MAX: (libc)Utility Limits.
* BC_STRING_MAX: (libc)Utility Limits.
* BRKINT: (libc)Input Modes.
* BUFSIZ: (libc)Controlling Buffering.
* CCTS_OFLOW: (libc)Control Modes.
* CHILD_MAX: (libc)General Limits.
* CIGNORE: (libc)Control Modes.
* CLK_TCK: (libc)CPU Time.
* CLOCAL: (libc)Control Modes.
* CLOCKS_PER_SEC: (libc)CPU Time.
* COLL_WEIGHTS_MAX: (libc)Utility Limits.
* CPU_CLR: (libc)CPU Affinity.
* CPU_ISSET: (libc)CPU Affinity.
* CPU_SET: (libc)CPU Affinity.
* CPU_SETSIZE: (libc)CPU Affinity.
* CPU_ZERO: (libc)CPU Affinity.
* CREAD: (libc)Control Modes.
* CRTS_IFLOW: (libc)Control Modes.
* CS5: (libc)Control Modes.
* CS6: (libc)Control Modes.
* CS7: (libc)Control Modes.
* CS8: (libc)Control Modes.
* CSIZE: (libc)Control Modes.
* CSTOPB: (libc)Control Modes.
* DES_FAILED: (libc)DES Encryption.
* DTTOIF: (libc)Directory Entries.
* E2BIG: (libc)Error Codes.
* EACCES: (libc)Error Codes.
* EADDRINUSE: (libc)Error Codes.
* EADDRNOTAVAIL: (libc)Error Codes.
* EADV: (libc)Error Codes.
* EAFNOSUPPORT: (libc)Error Codes.
* EAGAIN: (libc)Error Codes.
* EALREADY: (libc)Error Codes.
* EAUTH: (libc)Error Codes.
* EBACKGROUND: (libc)Error Codes.
* EBADE: (libc)Error Codes.
* EBADF: (libc)Error Codes.
* EBADFD: (libc)Error Codes.
* EBADMSG: (libc)Error Codes.
* EBADR: (libc)Error Codes.
* EBADRPC: (libc)Error Codes.
* EBADRQC: (libc)Error Codes.
* EBADSLT: (libc)Error Codes.
* EBFONT: (libc)Error Codes.
* EBUSY: (libc)Error Codes.
* ECANCELED: (libc)Error Codes.
* ECHILD: (libc)Error Codes.
* ECHO: (libc)Local Modes.
* ECHOCTL: (libc)Local Modes.
* ECHOE: (libc)Local Modes.
* ECHOK: (libc)Local Modes.
* ECHOKE: (libc)Local Modes.
* ECHONL: (libc)Local Modes.
* ECHOPRT: (libc)Local Modes.
* ECHRNG: (libc)Error Codes.
* ECOMM: (libc)Error Codes.
* ECONNABORTED: (libc)Error Codes.
* ECONNREFUSED: (libc)Error Codes.
* ECONNRESET: (libc)Error Codes.
* ED: (libc)Error Codes.
* EDEADLK: (libc)Error Codes.
* EDEADLOCK: (libc)Error Codes.
* EDESTADDRREQ: (libc)Error Codes.
* EDIED: (libc)Error Codes.
* EDOM: (libc)Error Codes.
* EDOTDOT: (libc)Error Codes.
* EDQUOT: (libc)Error Codes.
* EEXIST: (libc)Error Codes.
* EFAULT: (libc)Error Codes.
* EFBIG: (libc)Error Codes.
* EFTYPE: (libc)Error Codes.
* EGRATUITOUS: (libc)Error Codes.
* EGREGIOUS: (libc)Error Codes.
* EHOSTDOWN: (libc)Error Codes.
* EHOSTUNREACH: (libc)Error Codes.
* EIDRM: (libc)Error Codes.
* EIEIO: (libc)Error Codes.
* EILSEQ: (libc)Error Codes.
* EINPROGRESS: (libc)Error Codes.
* EINTR: (libc)Error Codes.
* EINVAL: (libc)Error Codes.
* EIO: (libc)Error Codes.
* EISCONN: (libc)Error Codes.
* EISDIR: (libc)Error Codes.
* EISNAM: (libc)Error Codes.
* EL2HLT: (libc)Error Codes.
* EL2NSYNC: (libc)Error Codes.
* EL3HLT: (libc)Error Codes.
* EL3RST: (libc)Error Codes.
* ELIBACC: (libc)Error Codes.
* ELIBBAD: (libc)Error Codes.
* ELIBEXEC: (libc)Error Codes.
* ELIBMAX: (libc)Error Codes.
* ELIBSCN: (libc)Error Codes.
* ELNRNG: (libc)Error Codes.
* ELOOP: (libc)Error Codes.
* EMEDIUMTYPE: (libc)Error Codes.
* EMFILE: (libc)Error Codes.
* EMLINK: (libc)Error Codes.
* EMSGSIZE: (libc)Error Codes.
* EMULTIHOP: (libc)Error Codes.
* ENAMETOOLONG: (libc)Error Codes.
* ENAVAIL: (libc)Error Codes.
* ENEEDAUTH: (libc)Error Codes.
* ENETDOWN: (libc)Error Codes.
* ENETRESET: (libc)Error Codes.
* ENETUNREACH: (libc)Error Codes.
* ENFILE: (libc)Error Codes.
* ENOANO: (libc)Error Codes.
* ENOBUFS: (libc)Error Codes.
* ENOCSI: (libc)Error Codes.
* ENODATA: (libc)Error Codes.
* ENODEV: (libc)Error Codes.
* ENOENT: (libc)Error Codes.
* ENOEXEC: (libc)Error Codes.
* ENOLCK: (libc)Error Codes.
* ENOLINK: (libc)Error Codes.
* ENOMEDIUM: (libc)Error Codes.
* ENOMEM: (libc)Error Codes.
* ENOMSG: (libc)Error Codes.
* ENONET: (libc)Error Codes.
* ENOPKG: (libc)Error Codes.
* ENOPROTOOPT: (libc)Error Codes.
* ENOSPC: (libc)Error Codes.
* ENOSR: (libc)Error Codes.
* ENOSTR: (libc)Error Codes.
* ENOSYS: (libc)Error Codes.
* ENOTBLK: (libc)Error Codes.
* ENOTCONN: (libc)Error Codes.
* ENOTDIR: (libc)Error Codes.
* ENOTEMPTY: (libc)Error Codes.
* ENOTNAM: (libc)Error Codes.
* ENOTSOCK: (libc)Error Codes.
* ENOTSUP: (libc)Error Codes.
* ENOTTY: (libc)Error Codes.
* ENOTUNIQ: (libc)Error Codes.
* ENXIO: (libc)Error Codes.
* EOF: (libc)EOF and Errors.
* EOPNOTSUPP: (libc)Error Codes.
* EOVERFLOW: (libc)Error Codes.
* EPERM: (libc)Error Codes.
* EPFNOSUPPORT: (libc)Error Codes.
* EPIPE: (libc)Error Codes.
* EPROCLIM: (libc)Error Codes.
* EPROCUNAVAIL: (libc)Error Codes.
* EPROGMISMATCH: (libc)Error Codes.
* EPROGUNAVAIL: (libc)Error Codes.
* EPROTO: (libc)Error Codes.
* EPROTONOSUPPORT: (libc)Error Codes.
* EPROTOTYPE: (libc)Error Codes.
* EQUIV_CLASS_MAX: (libc)Utility Limits.
* ERANGE: (libc)Error Codes.
* EREMCHG: (libc)Error Codes.
* EREMOTE: (libc)Error Codes.
* EREMOTEIO: (libc)Error Codes.
* ERESTART: (libc)Error Codes.
* EROFS: (libc)Error Codes.
* ERPCMISMATCH: (libc)Error Codes.
* ESHUTDOWN: (libc)Error Codes.
* ESOCKTNOSUPPORT: (libc)Error Codes.
* ESPIPE: (libc)Error Codes.
* ESRCH: (libc)Error Codes.
* ESRMNT: (libc)Error Codes.
* ESTALE: (libc)Error Codes.
* ESTRPIPE: (libc)Error Codes.
* ETIME: (libc)Error Codes.
* ETIMEDOUT: (libc)Error Codes.
* ETOOMANYREFS: (libc)Error Codes.
* ETXTBSY: (libc)Error Codes.
* EUCLEAN: (libc)Error Codes.
* EUNATCH: (libc)Error Codes.
* EUSERS: (libc)Error Codes.
* EWOULDBLOCK: (libc)Error Codes.
* EXDEV: (libc)Error Codes.
* EXFULL: (libc)Error Codes.
* EXIT_FAILURE: (libc)Exit Status.
* EXIT_SUCCESS: (libc)Exit Status.
* EXPR_NEST_MAX: (libc)Utility Limits.
* FD_CLOEXEC: (libc)Descriptor Flags.
* FD_CLR: (libc)Waiting for I/O.
* FD_ISSET: (libc)Waiting for I/O.
* FD_SET: (libc)Waiting for I/O.
* FD_SETSIZE: (libc)Waiting for I/O.
* FD_ZERO: (libc)Waiting for I/O.
* FILENAME_MAX: (libc)Limits for Files.
* FLUSHO: (libc)Local Modes.
* FOPEN_MAX: (libc)Opening Streams.
* FP_ILOGB0: (libc)Exponents and Logarithms.
* FP_ILOGBNAN: (libc)Exponents and Logarithms.
* F_DUPFD: (libc)Duplicating Descriptors.
* F_GETFD: (libc)Descriptor Flags.
* F_GETFL: (libc)Getting File Status Flags.
* F_GETLK: (libc)File Locks.
* F_GETOWN: (libc)Interrupt Input.
* F_OK: (libc)Testing File Access.
* F_SETFD: (libc)Descriptor Flags.
* F_SETFL: (libc)Getting File Status Flags.
* F_SETLK: (libc)File Locks.
* F_SETLKW: (libc)File Locks.
* F_SETOWN: (libc)Interrupt Input.
* HUGE_VAL: (libc)Math Error Reporting.
* HUGE_VALF: (libc)Math Error Reporting.
* HUGE_VALL: (libc)Math Error Reporting.
* HUPCL: (libc)Control Modes.
* I: (libc)Complex Numbers.
* ICANON: (libc)Local Modes.
* ICRNL: (libc)Input Modes.
* IEXTEN: (libc)Local Modes.
* IFNAMSIZ: (libc)Interface Naming.
* IFTODT: (libc)Directory Entries.
* IGNBRK: (libc)Input Modes.
* IGNCR: (libc)Input Modes.
* IGNPAR: (libc)Input Modes.
* IMAXBEL: (libc)Input Modes.
* INADDR_ANY: (libc)Host Address Data Type.
* INADDR_BROADCAST: (libc)Host Address Data Type.
* INADDR_LOOPBACK: (libc)Host Address Data Type.
* INADDR_NONE: (libc)Host Address Data Type.
* INFINITY: (libc)Infinity and NaN.
* INLCR: (libc)Input Modes.
* INPCK: (libc)Input Modes.
* IPPORT_RESERVED: (libc)Ports.
* IPPORT_USERRESERVED: (libc)Ports.
* ISIG: (libc)Local Modes.
* ISTRIP: (libc)Input Modes.
* IXANY: (libc)Input Modes.
* IXOFF: (libc)Input Modes.
* IXON: (libc)Input Modes.
* LINE_MAX: (libc)Utility Limits.
* LINK_MAX: (libc)Limits for Files.
* L_ctermid: (libc)Identifying the Terminal.
* L_cuserid: (libc)Who Logged In.
* L_tmpnam: (libc)Temporary Files.
* MAXNAMLEN: (libc)Limits for Files.
* MAXSYMLINKS: (libc)Symbolic Links.
* MAX_CANON: (libc)Limits for Files.
* MAX_INPUT: (libc)Limits for Files.
* MB_CUR_MAX: (libc)Selecting the Conversion.
* MB_LEN_MAX: (libc)Selecting the Conversion.
* MDMBUF: (libc)Control Modes.
* MSG_DONTROUTE: (libc)Socket Data Options.
* MSG_OOB: (libc)Socket Data Options.
* MSG_PEEK: (libc)Socket Data Options.
* NAME_MAX: (libc)Limits for Files.
* NAN: (libc)Infinity and NaN.
* NCCS: (libc)Mode Data Types.
* NGROUPS_MAX: (libc)General Limits.
* NOFLSH: (libc)Local Modes.
* NOKERNINFO: (libc)Local Modes.
* NSIG: (libc)Standard Signals.
* NULL: (libc)Null Pointer Constant.
* ONLCR: (libc)Output Modes.
* ONOEOT: (libc)Output Modes.
* OPEN_MAX: (libc)General Limits.
* OPOST: (libc)Output Modes.
* OXTABS: (libc)Output Modes.
* O_ACCMODE: (libc)Access Modes.
* O_APPEND: (libc)Operating Modes.
* O_ASYNC: (libc)Operating Modes.
* O_CREAT: (libc)Open-time Flags.
* O_EXCL: (libc)Open-time Flags.
* O_EXEC: (libc)Access Modes.
* O_EXLOCK: (libc)Open-time Flags.
* O_FSYNC: (libc)Operating Modes.
* O_IGNORE_CTTY: (libc)Open-time Flags.
* O_NDELAY: (libc)Operating Modes.
* O_NOATIME: (libc)Operating Modes.
* O_NOCTTY: (libc)Open-time Flags.
* O_NOLINK: (libc)Open-time Flags.
* O_NONBLOCK: (libc)Open-time Flags.
* O_NONBLOCK: (libc)Operating Modes.
* O_NOTRANS: (libc)Open-time Flags.
* O_RDONLY: (libc)Access Modes.
* O_RDWR: (libc)Access Modes.
* O_READ: (libc)Access Modes.
* O_SHLOCK: (libc)Open-time Flags.
* O_SYNC: (libc)Operating Modes.
* O_TRUNC: (libc)Open-time Flags.
* O_WRITE: (libc)Access Modes.
* O_WRONLY: (libc)Access Modes.
* PARENB: (libc)Control Modes.
* PARMRK: (libc)Input Modes.
* PARODD: (libc)Control Modes.
* PATH_MAX: (libc)Limits for Files.
* PA_FLAG_MASK: (libc)Parsing a Template String.
* PENDIN: (libc)Local Modes.
* PF_FILE: (libc)Local Namespace Details.
* PF_INET6: (libc)Internet Namespace.
* PF_INET: (libc)Internet Namespace.
* PF_LOCAL: (libc)Local Namespace Details.
* PF_UNIX: (libc)Local Namespace Details.
* PIPE_BUF: (libc)Limits for Files.
* P_tmpdir: (libc)Temporary Files.
* RAND_MAX: (libc)ISO Random.
* RE_DUP_MAX: (libc)General Limits.
* RLIM_INFINITY: (libc)Limits on Resources.
* R_OK: (libc)Testing File Access.
* SA_NOCLDSTOP: (libc)Flags for Sigaction.
* SA_ONSTACK: (libc)Flags for Sigaction.
* SA_RESTART: (libc)Flags for Sigaction.
* SEEK_CUR: (libc)File Positioning.
* SEEK_END: (libc)File Positioning.
* SEEK_SET: (libc)File Positioning.
* SIGABRT: (libc)Program Error Signals.
* SIGALRM: (libc)Alarm Signals.
* SIGBUS: (libc)Program Error Signals.
* SIGCHLD: (libc)Job Control Signals.
* SIGCLD: (libc)Job Control Signals.
* SIGCONT: (libc)Job Control Signals.
* SIGEMT: (libc)Program Error Signals.
* SIGFPE: (libc)Program Error Signals.
* SIGHUP: (libc)Termination Signals.
* SIGILL: (libc)Program Error Signals.
* SIGINFO: (libc)Miscellaneous Signals.
* SIGINT: (libc)Termination Signals.
* SIGIO: (libc)Asynchronous I/O Signals.
* SIGIOT: (libc)Program Error Signals.
* SIGKILL: (libc)Termination Signals.
* SIGLOST: (libc)Operation Error Signals.
* SIGPIPE: (libc)Operation Error Signals.
* SIGPOLL: (libc)Asynchronous I/O Signals.
* SIGPROF: (libc)Alarm Signals.
* SIGQUIT: (libc)Termination Signals.
* SIGSEGV: (libc)Program Error Signals.
* SIGSTOP: (libc)Job Control Signals.
* SIGSYS: (libc)Program Error Signals.
* SIGTERM: (libc)Termination Signals.
* SIGTRAP: (libc)Program Error Signals.
* SIGTSTP: (libc)Job Control Signals.
* SIGTTIN: (libc)Job Control Signals.
* SIGTTOU: (libc)Job Control Signals.
* SIGURG: (libc)Asynchronous I/O Signals.
* SIGUSR1: (libc)Miscellaneous Signals.
* SIGUSR2: (libc)Miscellaneous Signals.
* SIGVTALRM: (libc)Alarm Signals.
* SIGWINCH: (libc)Miscellaneous Signals.
* SIGXCPU: (libc)Operation Error Signals.
* SIGXFSZ: (libc)Operation Error Signals.
* SIG_ERR: (libc)Basic Signal Handling.
* SOCK_DGRAM: (libc)Communication Styles.
* SOCK_RAW: (libc)Communication Styles.
* SOCK_RDM: (libc)Communication Styles.
* SOCK_SEQPACKET: (libc)Communication Styles.
* SOCK_STREAM: (libc)Communication Styles.
* SOL_SOCKET: (libc)Socket-Level Options.
* SSIZE_MAX: (libc)General Limits.
* STREAM_MAX: (libc)General Limits.
* SUN_LEN: (libc)Local Namespace Details.
* SV_INTERRUPT: (libc)BSD Handler.
* SV_ONSTACK: (libc)BSD Handler.
* SV_RESETHAND: (libc)BSD Handler.
* S_IFMT: (libc)Testing File Type.
* S_ISBLK: (libc)Testing File Type.
* S_ISCHR: (libc)Testing File Type.
* S_ISDIR: (libc)Testing File Type.
* S_ISFIFO: (libc)Testing File Type.
* S_ISLNK: (libc)Testing File Type.
* S_ISREG: (libc)Testing File Type.
* S_ISSOCK: (libc)Testing File Type.
* S_TYPEISMQ: (libc)Testing File Type.
* S_TYPEISSEM: (libc)Testing File Type.
* S_TYPEISSHM: (libc)Testing File Type.
* TMP_MAX: (libc)Temporary Files.
* TOSTOP: (libc)Local Modes.
* TZNAME_MAX: (libc)General Limits.
* VDISCARD: (libc)Other Special.
* VDSUSP: (libc)Signal Characters.
* VEOF: (libc)Editing Characters.
* VEOL2: (libc)Editing Characters.
* VEOL: (libc)Editing Characters.
* VERASE: (libc)Editing Characters.
* VINTR: (libc)Signal Characters.
* VKILL: (libc)Editing Characters.
* VLNEXT: (libc)Other Special.
* VMIN: (libc)Noncanonical Input.
* VQUIT: (libc)Signal Characters.
* VREPRINT: (libc)Editing Characters.
* VSTART: (libc)Start/Stop Characters.
* VSTATUS: (libc)Other Special.
* VSTOP: (libc)Start/Stop Characters.
* VSUSP: (libc)Signal Characters.
* VTIME: (libc)Noncanonical Input.
* VWERASE: (libc)Editing Characters.
* WCHAR_MAX: (libc)Extended Char Intro.
* WCHAR_MIN: (libc)Extended Char Intro.
* WCOREDUMP: (libc)Process Completion Status.
* WEOF: (libc)EOF and Errors.
* WEOF: (libc)Extended Char Intro.
* WEXITSTATUS: (libc)Process Completion Status.
* WIFEXITED: (libc)Process Completion Status.
* WIFSIGNALED: (libc)Process Completion Status.
* WIFSTOPPED: (libc)Process Completion Status.
* WSTOPSIG: (libc)Process Completion Status.
* WTERMSIG: (libc)Process Completion Status.
* W_OK: (libc)Testing File Access.
* X_OK: (libc)Testing File Access.
* _Complex_I: (libc)Complex Numbers.
* _Exit: (libc)Termination Internals.
* _IOFBF: (libc)Controlling Buffering.
* _IOLBF: (libc)Controlling Buffering.
* _IONBF: (libc)Controlling Buffering.
* _Imaginary_I: (libc)Complex Numbers.
* _PATH_UTMP: (libc)Manipulating the Database.
* _PATH_WTMP: (libc)Manipulating the Database.
* _POSIX2_C_DEV: (libc)System Options.
* _POSIX2_C_VERSION: (libc)Version Supported.
* _POSIX2_FORT_DEV: (libc)System Options.
* _POSIX2_FORT_RUN: (libc)System Options.
* _POSIX2_LOCALEDEF: (libc)System Options.
* _POSIX2_SW_DEV: (libc)System Options.
* _POSIX_CHOWN_RESTRICTED: (libc)Options for Files.
* _POSIX_JOB_CONTROL: (libc)System Options.
* _POSIX_NO_TRUNC: (libc)Options for Files.
* _POSIX_SAVED_IDS: (libc)System Options.
* _POSIX_VDISABLE: (libc)Options for Files.
* _POSIX_VERSION: (libc)Version Supported.
* __fbufsize: (libc)Controlling Buffering.
* __flbf: (libc)Controlling Buffering.
* __fpending: (libc)Controlling Buffering.
* __fpurge: (libc)Flushing Buffers.
* __freadable: (libc)Opening Streams.
* __freading: (libc)Opening Streams.
* __fsetlocking: (libc)Streams and Threads.
* __fwritable: (libc)Opening Streams.
* __fwriting: (libc)Opening Streams.
* __gconv_end_fct: (libc)glibc iconv Implementation.
* __gconv_fct: (libc)glibc iconv Implementation.
* __gconv_init_fct: (libc)glibc iconv Implementation.
* __va_copy: (libc)Argument Macros.
* _exit: (libc)Termination Internals.
* _flushlbf: (libc)Flushing Buffers.
* _tolower: (libc)Case Conversion.
* _toupper: (libc)Case Conversion.
* a64l: (libc)Encode Binary Data.
* abort: (libc)Aborting a Program.
* abs: (libc)Absolute Value.
* accept: (libc)Accepting Connections.
* access: (libc)Testing File Access.
* acos: (libc)Inverse Trig Functions.
* acosf: (libc)Inverse Trig Functions.
* acosh: (libc)Hyperbolic Functions.
* acoshf: (libc)Hyperbolic Functions.
* acoshl: (libc)Hyperbolic Functions.
* acosl: (libc)Inverse Trig Functions.
* addmntent: (libc)mtab.
* addseverity: (libc)Adding Severity Classes.
* adjtime: (libc)High-Resolution Calendar.
* adjtimex: (libc)High-Resolution Calendar.
* aio_cancel64: (libc)Cancel AIO Operations.
* aio_cancel: (libc)Cancel AIO Operations.
* aio_error64: (libc)Status of AIO Operations.
* aio_error: (libc)Status of AIO Operations.
* aio_fsync64: (libc)Synchronizing AIO Operations.
* aio_fsync: (libc)Synchronizing AIO Operations.
* aio_init: (libc)Configuration of AIO.
* aio_read64: (libc)Asynchronous Reads/Writes.
* aio_read: (libc)Asynchronous Reads/Writes.
* aio_return64: (libc)Status of AIO Operations.
* aio_return: (libc)Status of AIO Operations.
* aio_suspend64: (libc)Synchronizing AIO Operations.
* aio_suspend: (libc)Synchronizing AIO Operations.
* aio_write64: (libc)Asynchronous Reads/Writes.
* aio_write: (libc)Asynchronous Reads/Writes.
* alarm: (libc)Setting an Alarm.
* alloca: (libc)Variable Size Automatic.
* alphasort64: (libc)Scanning Directory Content.
* alphasort: (libc)Scanning Directory Content.
* argp_error: (libc)Argp Helper Functions.
* argp_failure: (libc)Argp Helper Functions.
* argp_help: (libc)Argp Help.
* argp_parse: (libc)Argp.
* argp_state_help: (libc)Argp Helper Functions.
* argp_usage: (libc)Argp Helper Functions.
* argz_add: (libc)Argz Functions.
* argz_add_sep: (libc)Argz Functions.
* argz_append: (libc)Argz Functions.
* argz_count: (libc)Argz Functions.
* argz_create: (libc)Argz Functions.
* argz_create_sep: (libc)Argz Functions.
* argz_delete: (libc)Argz Functions.
* argz_extract: (libc)Argz Functions.
* argz_insert: (libc)Argz Functions.
* argz_next: (libc)Argz Functions.
* argz_replace: (libc)Argz Functions.
* argz_stringify: (libc)Argz Functions.
* asctime: (libc)Formatting Calendar Time.
* asctime_r: (libc)Formatting Calendar Time.
* asin: (libc)Inverse Trig Functions.
* asinf: (libc)Inverse Trig Functions.
* asinh: (libc)Hyperbolic Functions.
* asinhf: (libc)Hyperbolic Functions.
* asinhl: (libc)Hyperbolic Functions.
* asinl: (libc)Inverse Trig Functions.
* asprintf: (libc)Dynamic Output.
* assert: (libc)Consistency Checking.
* assert_perror: (libc)Consistency Checking.
* atan2: (libc)Inverse Trig Functions.
* atan2f: (libc)Inverse Trig Functions.
* atan2l: (libc)Inverse Trig Functions.
* atan: (libc)Inverse Trig Functions.
* atanf: (libc)Inverse Trig Functions.
* atanh: (libc)Hyperbolic Functions.
* atanhf: (libc)Hyperbolic Functions.
* atanhl: (libc)Hyperbolic Functions.
* atanl: (libc)Inverse Trig Functions.
* atexit: (libc)Cleanups on Exit.
* atof: (libc)Parsing of Floats.
* atoi: (libc)Parsing of Integers.
* atol: (libc)Parsing of Integers.
* atoll: (libc)Parsing of Integers.
* backtrace: (libc)Backtraces.
* backtrace_symbols: (libc)Backtraces.
* backtrace_symbols_fd: (libc)Backtraces.
* basename: (libc)Finding Tokens in a String.
* basename: (libc)Finding Tokens in a String.
* bcmp: (libc)String/Array Comparison.
* bcopy: (libc)Copying and Concatenation.
* bind: (libc)Setting Address.
* bind_textdomain_codeset: (libc)Charset conversion in gettext.
* bindtextdomain: (libc)Locating gettext catalog.
* brk: (libc)Resizing the Data Segment.
* bsearch: (libc)Array Search Function.
* btowc: (libc)Converting a Character.
* bzero: (libc)Copying and Concatenation.
* cabs: (libc)Absolute Value.
* cabsf: (libc)Absolute Value.
* cabsl: (libc)Absolute Value.
* cacos: (libc)Inverse Trig Functions.
* cacosf: (libc)Inverse Trig Functions.
* cacosh: (libc)Hyperbolic Functions.
* cacoshf: (libc)Hyperbolic Functions.
* cacoshl: (libc)Hyperbolic Functions.
* cacosl: (libc)Inverse Trig Functions.
* calloc: (libc)Allocating Cleared Space.
* canonicalize_file_name: (libc)Symbolic Links.
* carg: (libc)Operations on Complex.
* cargf: (libc)Operations on Complex.
* cargl: (libc)Operations on Complex.
* casin: (libc)Inverse Trig Functions.
* casinf: (libc)Inverse Trig Functions.
* casinh: (libc)Hyperbolic Functions.
* casinhf: (libc)Hyperbolic Functions.
* casinhl: (libc)Hyperbolic Functions.
* casinl: (libc)Inverse Trig Functions.
* catan: (libc)Inverse Trig Functions.
* catanf: (libc)Inverse Trig Functions.
* catanh: (libc)Hyperbolic Functions.
* catanhf: (libc)Hyperbolic Functions.
* catanhl: (libc)Hyperbolic Functions.
* catanl: (libc)Inverse Trig Functions.
* catclose: (libc)The catgets Functions.
* catgets: (libc)The catgets Functions.
* catopen: (libc)The catgets Functions.
* cbc_crypt: (libc)DES Encryption.
* cbrt: (libc)Exponents and Logarithms.
* cbrtf: (libc)Exponents and Logarithms.
* cbrtl: (libc)Exponents and Logarithms.
* ccos: (libc)Trig Functions.
* ccosf: (libc)Trig Functions.
* ccosh: (libc)Hyperbolic Functions.
* ccoshf: (libc)Hyperbolic Functions.
* ccoshl: (libc)Hyperbolic Functions.
* ccosl: (libc)Trig Functions.
* ceil: (libc)Rounding Functions.
* ceilf: (libc)Rounding Functions.
* ceill: (libc)Rounding Functions.
* cexp: (libc)Exponents and Logarithms.
* cexpf: (libc)Exponents and Logarithms.
* cexpl: (libc)Exponents and Logarithms.
* cfgetispeed: (libc)Line Speed.
* cfgetospeed: (libc)Line Speed.
* cfmakeraw: (libc)Noncanonical Input.
* cfree: (libc)Freeing after Malloc.
* cfsetispeed: (libc)Line Speed.
* cfsetospeed: (libc)Line Speed.
* cfsetspeed: (libc)Line Speed.
* chdir: (libc)Working Directory.
* chmod: (libc)Setting Permissions.
* chown: (libc)File Owner.
* cimag: (libc)Operations on Complex.
* cimagf: (libc)Operations on Complex.
* cimagl: (libc)Operations on Complex.
* clearenv: (libc)Environment Access.
* clearerr: (libc)Error Recovery.
* clearerr_unlocked: (libc)Error Recovery.
* clock: (libc)CPU Time.
* clog10: (libc)Exponents and Logarithms.
* clog10f: (libc)Exponents and Logarithms.
* clog10l: (libc)Exponents and Logarithms.
* clog: (libc)Exponents and Logarithms.
* clogf: (libc)Exponents and Logarithms.
* clogl: (libc)Exponents and Logarithms.
* close: (libc)Opening and Closing Files.
* closedir: (libc)Reading/Closing Directory.
* closelog: (libc)closelog.
* confstr: (libc)String Parameters.
* conj: (libc)Operations on Complex.
* conjf: (libc)Operations on Complex.
* conjl: (libc)Operations on Complex.
* connect: (libc)Connecting.
* copysign: (libc)FP Bit Twiddling.
* copysignf: (libc)FP Bit Twiddling.
* copysignl: (libc)FP Bit Twiddling.
* cos: (libc)Trig Functions.
* cosf: (libc)Trig Functions.
* cosh: (libc)Hyperbolic Functions.
* coshf: (libc)Hyperbolic Functions.
* coshl: (libc)Hyperbolic Functions.
* cosl: (libc)Trig Functions.
* cpow: (libc)Exponents and Logarithms.
* cpowf: (libc)Exponents and Logarithms.
* cpowl: (libc)Exponents and Logarithms.
* cproj: (libc)Operations on Complex.
* cprojf: (libc)Operations on Complex.
* cprojl: (libc)Operations on Complex.
* creal: (libc)Operations on Complex.
* crealf: (libc)Operations on Complex.
* creall: (libc)Operations on Complex.
* creat64: (libc)Opening and Closing Files.
* creat: (libc)Opening and Closing Files.
* crypt: (libc)crypt.
* crypt_r: (libc)crypt.
* csin: (libc)Trig Functions.
* csinf: (libc)Trig Functions.
* csinh: (libc)Hyperbolic Functions.
* csinhf: (libc)Hyperbolic Functions.
* csinhl: (libc)Hyperbolic Functions.
* csinl: (libc)Trig Functions.
* csqrt: (libc)Exponents and Logarithms.
* csqrtf: (libc)Exponents and Logarithms.
* csqrtl: (libc)Exponents and Logarithms.
* ctan: (libc)Trig Functions.
* ctanf: (libc)Trig Functions.
* ctanh: (libc)Hyperbolic Functions.
* ctanhf: (libc)Hyperbolic Functions.
* ctanhl: (libc)Hyperbolic Functions.
* ctanl: (libc)Trig Functions.
* ctermid: (libc)Identifying the Terminal.
* ctime: (libc)Formatting Calendar Time.
* ctime_r: (libc)Formatting Calendar Time.
* cuserid: (libc)Who Logged In.
* dcgettext: (libc)Translation with gettext.
* dcngettext: (libc)Advanced gettext functions.
* des_setparity: (libc)DES Encryption.
* dgettext: (libc)Translation with gettext.
* difftime: (libc)Elapsed Time.
* dirfd: (libc)Opening a Directory.
* dirname: (libc)Finding Tokens in a String.
* div: (libc)Integer Division.
* dngettext: (libc)Advanced gettext functions.
* drand48: (libc)SVID Random.
* drand48_r: (libc)SVID Random.
* drem: (libc)Remainder Functions.
* dremf: (libc)Remainder Functions.
* dreml: (libc)Remainder Functions.
* dup2: (libc)Duplicating Descriptors.
* dup: (libc)Duplicating Descriptors.
* ecb_crypt: (libc)DES Encryption.
* ecvt: (libc)System V Number Conversion.
* ecvt_r: (libc)System V Number Conversion.
* encrypt: (libc)DES Encryption.
* encrypt_r: (libc)DES Encryption.
* endfsent: (libc)fstab.
* endgrent: (libc)Scanning All Groups.
* endhostent: (libc)Host Names.
* endmntent: (libc)mtab.
* endnetent: (libc)Networks Database.
* endnetgrent: (libc)Lookup Netgroup.
* endprotoent: (libc)Protocols Database.
* endpwent: (libc)Scanning All Users.
* endservent: (libc)Services Database.
* endutent: (libc)Manipulating the Database.
* endutxent: (libc)XPG Functions.
* envz_add: (libc)Envz Functions.
* envz_entry: (libc)Envz Functions.
* envz_get: (libc)Envz Functions.
* envz_merge: (libc)Envz Functions.
* envz_strip: (libc)Envz Functions.
* erand48: (libc)SVID Random.
* erand48_r: (libc)SVID Random.
* erf: (libc)Special Functions.
* erfc: (libc)Special Functions.
* erfcf: (libc)Special Functions.
* erfcl: (libc)Special Functions.
* erff: (libc)Special Functions.
* erfl: (libc)Special Functions.
* err: (libc)Error Messages.
* errno: (libc)Checking for Errors.
* error: (libc)Error Messages.
* error_at_line: (libc)Error Messages.
* errx: (libc)Error Messages.
* execl: (libc)Executing a File.
* execle: (libc)Executing a File.
* execlp: (libc)Executing a File.
* execv: (libc)Executing a File.
* execve: (libc)Executing a File.
* execvp: (libc)Executing a File.
* exit: (libc)Normal Termination.
* exp10: (libc)Exponents and Logarithms.
* exp10f: (libc)Exponents and Logarithms.
* exp10l: (libc)Exponents and Logarithms.
* exp2: (libc)Exponents and Logarithms.
* exp2f: (libc)Exponents and Logarithms.
* exp2l: (libc)Exponents and Logarithms.
* exp: (libc)Exponents and Logarithms.
* expf: (libc)Exponents and Logarithms.
* expl: (libc)Exponents and Logarithms.
* expm1: (libc)Exponents and Logarithms.
* expm1f: (libc)Exponents and Logarithms.
* expm1l: (libc)Exponents and Logarithms.
* fabs: (libc)Absolute Value.
* fabsf: (libc)Absolute Value.
* fabsl: (libc)Absolute Value.
* fchdir: (libc)Working Directory.
* fchmod: (libc)Setting Permissions.
* fchown: (libc)File Owner.
* fclean: (libc)Cleaning Streams.
* fclose: (libc)Closing Streams.
* fcloseall: (libc)Closing Streams.
* fcntl: (libc)Control Operations.
* fcvt: (libc)System V Number Conversion.
* fcvt_r: (libc)System V Number Conversion.
* fdatasync: (libc)Synchronizing I/O.
* fdim: (libc)Misc FP Arithmetic.
* fdimf: (libc)Misc FP Arithmetic.
* fdiml: (libc)Misc FP Arithmetic.
* fdopen: (libc)Descriptors and Streams.
* feclearexcept: (libc)Status bit operations.
* fedisableexcept: (libc)Control Functions.
* feenableexcept: (libc)Control Functions.
* fegetenv: (libc)Control Functions.
* fegetexcept: (libc)Control Functions.
* fegetexceptflag: (libc)Status bit operations.
* fegetround: (libc)Rounding.
* feholdexcept: (libc)Control Functions.
* feof: (libc)EOF and Errors.
* feof_unlocked: (libc)EOF and Errors.
* feraiseexcept: (libc)Status bit operations.
* ferror: (libc)EOF and Errors.
* ferror_unlocked: (libc)EOF and Errors.
* fesetenv: (libc)Control Functions.
* fesetexceptflag: (libc)Status bit operations.
* fesetround: (libc)Rounding.
* fetestexcept: (libc)Status bit operations.
* feupdateenv: (libc)Control Functions.
* fflush: (libc)Flushing Buffers.
* fflush_unlocked: (libc)Flushing Buffers.
* fgetc: (libc)Character Input.
* fgetc_unlocked: (libc)Character Input.
* fgetgrent: (libc)Scanning All Groups.
* fgetgrent_r: (libc)Scanning All Groups.
* fgetpos64: (libc)Portable Positioning.
* fgetpos: (libc)Portable Positioning.
* fgetpwent: (libc)Scanning All Users.
* fgetpwent_r: (libc)Scanning All Users.
* fgets: (libc)Line Input.
* fgets_unlocked: (libc)Line Input.
* fgetwc: (libc)Character Input.
* fgetwc_unlocked: (libc)Character Input.
* fgetws: (libc)Line Input.
* fgetws_unlocked: (libc)Line Input.
* fileno: (libc)Descriptors and Streams.
* fileno_unlocked: (libc)Descriptors and Streams.
* finite: (libc)Floating Point Classes.
* finitef: (libc)Floating Point Classes.
* finitel: (libc)Floating Point Classes.
* flockfile: (libc)Streams and Threads.
* floor: (libc)Rounding Functions.
* floorf: (libc)Rounding Functions.
* floorl: (libc)Rounding Functions.
* fma: (libc)Misc FP Arithmetic.
* fmaf: (libc)Misc FP Arithmetic.
* fmal: (libc)Misc FP Arithmetic.
* fmax: (libc)Misc FP Arithmetic.
* fmaxf: (libc)Misc FP Arithmetic.
* fmaxl: (libc)Misc FP Arithmetic.
* fmemopen: (libc)String Streams.
* fmin: (libc)Misc FP Arithmetic.
* fminf: (libc)Misc FP Arithmetic.
* fminl: (libc)Misc FP Arithmetic.
* fmod: (libc)Remainder Functions.
* fmodf: (libc)Remainder Functions.
* fmodl: (libc)Remainder Functions.
* fmtmsg: (libc)Printing Formatted Messages.
* fnmatch: (libc)Wildcard Matching.
* fopen64: (libc)Opening Streams.
* fopen: (libc)Opening Streams.
* fopencookie: (libc)Streams and Cookies.
* fork: (libc)Creating a Process.
* forkpty: (libc)Pseudo-Terminal Pairs.
* fpathconf: (libc)Pathconf.
* fpclassify: (libc)Floating Point Classes.
* fprintf: (libc)Formatted Output Functions.
* fputc: (libc)Simple Output.
* fputc_unlocked: (libc)Simple Output.
* fputs: (libc)Simple Output.
* fputs_unlocked: (libc)Simple Output.
* fputwc: (libc)Simple Output.
* fputwc_unlocked: (libc)Simple Output.
* fputws: (libc)Simple Output.
* fputws_unlocked: (libc)Simple Output.
* fread: (libc)Block Input/Output.
* fread_unlocked: (libc)Block Input/Output.
* free: (libc)Freeing after Malloc.
* freopen64: (libc)Opening Streams.
* freopen: (libc)Opening Streams.
* frexp: (libc)Normalization Functions.
* frexpf: (libc)Normalization Functions.
* frexpl: (libc)Normalization Functions.
* fscanf: (libc)Formatted Input Functions.
* fseek: (libc)File Positioning.
* fseeko64: (libc)File Positioning.
* fseeko: (libc)File Positioning.
* fsetpos64: (libc)Portable Positioning.
* fsetpos: (libc)Portable Positioning.
* fstat64: (libc)Reading Attributes.
* fstat: (libc)Reading Attributes.
* fsync: (libc)Synchronizing I/O.
* ftell: (libc)File Positioning.
* ftello64: (libc)File Positioning.
* ftello: (libc)File Positioning.
* ftruncate64: (libc)File Size.
* ftruncate: (libc)File Size.
* ftrylockfile: (libc)Streams and Threads.
* ftw64: (libc)Working with Directory Trees.
* ftw: (libc)Working with Directory Trees.
* funlockfile: (libc)Streams and Threads.
* futimes: (libc)File Times.
* fwide: (libc)Streams and I18N.
* fwprintf: (libc)Formatted Output Functions.
* fwrite: (libc)Block Input/Output.
* fwrite_unlocked: (libc)Block Input/Output.
* fwscanf: (libc)Formatted Input Functions.
* gamma: (libc)Special Functions.
* gammaf: (libc)Special Functions.
* gammal: (libc)Special Functions.
* gcvt: (libc)System V Number Conversion.
* get_avphys_pages: (libc)Query Memory Parameters.
* get_current_dir_name: (libc)Working Directory.
* get_nprocs: (libc)Processor Resources.
* get_nprocs_conf: (libc)Processor Resources.
* get_phys_pages: (libc)Query Memory Parameters.
* getc: (libc)Character Input.
* getc_unlocked: (libc)Character Input.
* getchar: (libc)Character Input.
* getchar_unlocked: (libc)Character Input.
* getcontext: (libc)System V contexts.
* getcwd: (libc)Working Directory.
* getdate: (libc)General Time String Parsing.
* getdate_r: (libc)General Time String Parsing.
* getdelim: (libc)Line Input.
* getdomainnname: (libc)Host Identification.
* getegid: (libc)Reading Persona.
* getenv: (libc)Environment Access.
* geteuid: (libc)Reading Persona.
* getfsent: (libc)fstab.
* getfsfile: (libc)fstab.
* getfsspec: (libc)fstab.
* getgid: (libc)Reading Persona.
* getgrent: (libc)Scanning All Groups.
* getgrent_r: (libc)Scanning All Groups.
* getgrgid: (libc)Lookup Group.
* getgrgid_r: (libc)Lookup Group.
* getgrnam: (libc)Lookup Group.
* getgrnam_r: (libc)Lookup Group.
* getgrouplist: (libc)Setting Groups.
* getgroups: (libc)Reading Persona.
* gethostbyaddr: (libc)Host Names.
* gethostbyaddr_r: (libc)Host Names.
* gethostbyname2: (libc)Host Names.
* gethostbyname2_r: (libc)Host Names.
* gethostbyname: (libc)Host Names.
* gethostbyname_r: (libc)Host Names.
* gethostent: (libc)Host Names.
* gethostid: (libc)Host Identification.
* gethostname: (libc)Host Identification.
* getitimer: (libc)Setting an Alarm.
* getline: (libc)Line Input.
* getloadavg: (libc)Processor Resources.
* getlogin: (libc)Who Logged In.
* getmntent: (libc)mtab.
* getmntent_r: (libc)mtab.
* getnetbyaddr: (libc)Networks Database.
* getnetbyname: (libc)Networks Database.
* getnetent: (libc)Networks Database.
* getnetgrent: (libc)Lookup Netgroup.
* getnetgrent_r: (libc)Lookup Netgroup.
* getopt: (libc)Using Getopt.
* getopt_long: (libc)Getopt Long Options.
* getopt_long_only: (libc)Getopt Long Options.
* getpagesize: (libc)Query Memory Parameters.
* getpass: (libc)getpass.
* getpeername: (libc)Who is Connected.
* getpgid: (libc)Process Group Functions.
* getpgrp: (libc)Process Group Functions.
* getpgrp: (libc)Process Group Functions.
* getpid: (libc)Process Identification.
* getppid: (libc)Process Identification.
* getpriority: (libc)Traditional Scheduling Functions.
* getprotobyname: (libc)Protocols Database.
* getprotobynumber: (libc)Protocols Database.
* getprotoent: (libc)Protocols Database.
* getpt: (libc)Allocation.
* getpwent: (libc)Scanning All Users.
* getpwent_r: (libc)Scanning All Users.
* getpwnam: (libc)Lookup User.
* getpwnam_r: (libc)Lookup User.
* getpwuid: (libc)Lookup User.
* getpwuid_r: (libc)Lookup User.
* getrlimit64: (libc)Limits on Resources.
* getrlimit: (libc)Limits on Resources.
* getrusage: (libc)Resource Usage.
* gets: (libc)Line Input.
* getservbyname: (libc)Services Database.
* getservbyport: (libc)Services Database.
* getservent: (libc)Services Database.
* getsid: (libc)Process Group Functions.
* getsockname: (libc)Reading Address.
* getsockopt: (libc)Socket Option Functions.
* getsubopt: (libc)Suboptions.
* gettext: (libc)Translation with gettext.
* gettimeofday: (libc)High-Resolution Calendar.
* getuid: (libc)Reading Persona.
* getumask: (libc)Setting Permissions.
* getutent: (libc)Manipulating the Database.
* getutent_r: (libc)Manipulating the Database.
* getutid: (libc)Manipulating the Database.
* getutid_r: (libc)Manipulating the Database.
* getutline: (libc)Manipulating the Database.
* getutline_r: (libc)Manipulating the Database.
* getutmp: (libc)XPG Functions.
* getutmpx: (libc)XPG Functions.
* getutxent: (libc)XPG Functions.
* getutxid: (libc)XPG Functions.
* getutxline: (libc)XPG Functions.
* getw: (libc)Character Input.
* getwc: (libc)Character Input.
* getwc_unlocked: (libc)Character Input.
* getwchar: (libc)Character Input.
* getwchar_unlocked: (libc)Character Input.
* getwd: (libc)Working Directory.
* glob64: (libc)Calling Glob.
* glob: (libc)Calling Glob.
* globfree64: (libc)More Flags for Globbing.
* globfree: (libc)More Flags for Globbing.
* gmtime: (libc)Broken-down Time.
* gmtime_r: (libc)Broken-down Time.
* grantpt: (libc)Allocation.
* gsignal: (libc)Signaling Yourself.
* gtty: (libc)BSD Terminal Modes.
* hasmntopt: (libc)mtab.
* hcreate: (libc)Hash Search Function.
* hcreate_r: (libc)Hash Search Function.
* hdestroy: (libc)Hash Search Function.
* hdestroy_r: (libc)Hash Search Function.
* hsearch: (libc)Hash Search Function.
* hsearch_r: (libc)Hash Search Function.
* htonl: (libc)Byte Order.
* htons: (libc)Byte Order.
* hypot: (libc)Exponents and Logarithms.
* hypotf: (libc)Exponents and Logarithms.
* hypotl: (libc)Exponents and Logarithms.
* iconv: (libc)Generic Conversion Interface.
* iconv_close: (libc)Generic Conversion Interface.
* iconv_open: (libc)Generic Conversion Interface.
* if_freenameindex: (libc)Interface Naming.
* if_indextoname: (libc)Interface Naming.
* if_nameindex: (libc)Interface Naming.
* if_nametoindex: (libc)Interface Naming.
* ilogb: (libc)Exponents and Logarithms.
* ilogbf: (libc)Exponents and Logarithms.
* ilogbl: (libc)Exponents and Logarithms.
* imaxabs: (libc)Absolute Value.
* imaxdiv: (libc)Integer Division.
* in6addr_any: (libc)Host Address Data Type.
* in6addr_loopback: (libc)Host Address Data Type.
* index: (libc)Search Functions.
* inet_addr: (libc)Host Address Functions.
* inet_aton: (libc)Host Address Functions.
* inet_lnaof: (libc)Host Address Functions.
* inet_makeaddr: (libc)Host Address Functions.
* inet_netof: (libc)Host Address Functions.
* inet_network: (libc)Host Address Functions.
* inet_ntoa: (libc)Host Address Functions.
* inet_ntop: (libc)Host Address Functions.
* inet_pton: (libc)Host Address Functions.
* initgroups: (libc)Setting Groups.
* initstate: (libc)BSD Random.
* initstate_r: (libc)BSD Random.
* innetgr: (libc)Netgroup Membership.
* int: (libc)Random Access Directory.
* ioctl: (libc)IOCTLs.
* isalnum: (libc)Classification of Characters.
* isalpha: (libc)Classification of Characters.
* isascii: (libc)Classification of Characters.
* isatty: (libc)Is It a Terminal.
* isblank: (libc)Classification of Characters.
* iscntrl: (libc)Classification of Characters.
* isdigit: (libc)Classification of Characters.
* isfinite: (libc)Floating Point Classes.
* isgraph: (libc)Classification of Characters.
* isgreater: (libc)FP Comparison Functions.
* isgreaterequal: (libc)FP Comparison Functions.
* isinf: (libc)Floating Point Classes.
* isinff: (libc)Floating Point Classes.
* isinfl: (libc)Floating Point Classes.
* isless: (libc)FP Comparison Functions.
* islessequal: (libc)FP Comparison Functions.
* islessgreater: (libc)FP Comparison Functions.
* islower: (libc)Classification of Characters.
* isnan: (libc)Floating Point Classes.
* isnan: (libc)Floating Point Classes.
* isnanf: (libc)Floating Point Classes.
* isnanl: (libc)Floating Point Classes.
* isnormal: (libc)Floating Point Classes.
* isprint: (libc)Classification of Characters.
* ispunct: (libc)Classification of Characters.
* isspace: (libc)Classification of Characters.
* isunordered: (libc)FP Comparison Functions.
* isupper: (libc)Classification of Characters.
* iswalnum: (libc)Classification of Wide Characters.
* iswalpha: (libc)Classification of Wide Characters.
* iswblank: (libc)Classification of Wide Characters.
* iswcntrl: (libc)Classification of Wide Characters.
* iswctype: (libc)Classification of Wide Characters.
* iswdigit: (libc)Classification of Wide Characters.
* iswgraph: (libc)Classification of Wide Characters.
* iswlower: (libc)Classification of Wide Characters.
* iswprint: (libc)Classification of Wide Characters.
* iswpunct: (libc)Classification of Wide Characters.
* iswspace: (libc)Classification of Wide Characters.
* iswupper: (libc)Classification of Wide Characters.
* iswxdigit: (libc)Classification of Wide Characters.
* isxdigit: (libc)Classification of Characters.
* j0: (libc)Special Functions.
* j0f: (libc)Special Functions.
* j0l: (libc)Special Functions.
* j1: (libc)Special Functions.
* j1f: (libc)Special Functions.
* j1l: (libc)Special Functions.
* jn: (libc)Special Functions.
* jnf: (libc)Special Functions.
* jnl: (libc)Special Functions.
* jrand48: (libc)SVID Random.
* jrand48_r: (libc)SVID Random.
* kill: (libc)Signaling Another Process.
* killpg: (libc)Signaling Another Process.
* l64a: (libc)Encode Binary Data.
* labs: (libc)Absolute Value.
* lcong48: (libc)SVID Random.
* lcong48_r: (libc)SVID Random.
* ldexp: (libc)Normalization Functions.
* ldexpf: (libc)Normalization Functions.
* ldexpl: (libc)Normalization Functions.
* ldiv: (libc)Integer Division.
* lfind: (libc)Array Search Function.
* lgamma: (libc)Special Functions.
* lgamma_r: (libc)Special Functions.
* lgammaf: (libc)Special Functions.
* lgammaf_r: (libc)Special Functions.
* lgammal: (libc)Special Functions.
* lgammal_r: (libc)Special Functions.
* link: (libc)Hard Links.
* lio_listio64: (libc)Asynchronous Reads/Writes.
* lio_listio: (libc)Asynchronous Reads/Writes.
* listen: (libc)Listening.
* llabs: (libc)Absolute Value.
* lldiv: (libc)Integer Division.
* llrint: (libc)Rounding Functions.
* llrintf: (libc)Rounding Functions.
* llrintl: (libc)Rounding Functions.
* llround: (libc)Rounding Functions.
* llroundf: (libc)Rounding Functions.
* llroundl: (libc)Rounding Functions.
* localeconv: (libc)The Lame Way to Locale Data.
* localtime: (libc)Broken-down Time.
* localtime_r: (libc)Broken-down Time.
* log10: (libc)Exponents and Logarithms.
* log10f: (libc)Exponents and Logarithms.
* log10l: (libc)Exponents and Logarithms.
* log1p: (libc)Exponents and Logarithms.
* log1pf: (libc)Exponents and Logarithms.
* log1pl: (libc)Exponents and Logarithms.
* log2: (libc)Exponents and Logarithms.
* log2f: (libc)Exponents and Logarithms.
* log2l: (libc)Exponents and Logarithms.
* log: (libc)Exponents and Logarithms.
* logb: (libc)Exponents and Logarithms.
* logbf: (libc)Exponents and Logarithms.
* logbl: (libc)Exponents and Logarithms.
* logf: (libc)Exponents and Logarithms.
* login: (libc)Logging In and Out.
* login_tty: (libc)Logging In and Out.
* logl: (libc)Exponents and Logarithms.
* logout: (libc)Logging In and Out.
* logwtmp: (libc)Logging In and Out.
* longjmp: (libc)Non-Local Details.
* lrand48: (libc)SVID Random.
* lrand48_r: (libc)SVID Random.
* lrint: (libc)Rounding Functions.
* lrintf: (libc)Rounding Functions.
* lrintl: (libc)Rounding Functions.
* lround: (libc)Rounding Functions.
* lroundf: (libc)Rounding Functions.
* lroundl: (libc)Rounding Functions.
* lsearch: (libc)Array Search Function.
* lseek64: (libc)File Position Primitive.
* lseek: (libc)File Position Primitive.
* lstat64: (libc)Reading Attributes.
* lstat: (libc)Reading Attributes.
* lutimes: (libc)File Times.
* madvise: (libc)Memory-mapped I/O.
* makecontext: (libc)System V contexts.
* mallinfo: (libc)Statistics of Malloc.
* malloc: (libc)Basic Allocation.
* mallopt: (libc)Malloc Tunable Parameters.
* mblen: (libc)Non-reentrant Character Conversion.
* mbrlen: (libc)Converting a Character.
* mbrtowc: (libc)Converting a Character.
* mbsinit: (libc)Keeping the state.
* mbsnrtowcs: (libc)Converting Strings.
* mbsrtowcs: (libc)Converting Strings.
* mbstowcs: (libc)Non-reentrant String Conversion.
* mbtowc: (libc)Non-reentrant Character Conversion.
* mcheck: (libc)Heap Consistency Checking.
* memalign: (libc)Aligned Memory Blocks.
* memccpy: (libc)Copying and Concatenation.
* memchr: (libc)Search Functions.
* memcmp: (libc)String/Array Comparison.
* memcpy: (libc)Copying and Concatenation.
* memfrob: (libc)Trivial Encryption.
* memmem: (libc)Search Functions.
* memmove: (libc)Copying and Concatenation.
* mempcpy: (libc)Copying and Concatenation.
* memrchr: (libc)Search Functions.
* memset: (libc)Copying and Concatenation.
* mkdir: (libc)Creating Directories.
* mkdtemp: (libc)Temporary Files.
* mkfifo: (libc)FIFO Special Files.
* mknod: (libc)Making Special Files.
* mkstemp: (libc)Temporary Files.
* mktemp: (libc)Temporary Files.
* mktime: (libc)Broken-down Time.
* mlock: (libc)Page Lock Functions.
* mlockall: (libc)Page Lock Functions.
* mmap64: (libc)Memory-mapped I/O.
* mmap: (libc)Memory-mapped I/O.
* modf: (libc)Rounding Functions.
* modff: (libc)Rounding Functions.
* modfl: (libc)Rounding Functions.
* mount: (libc)Mount-Unmount-Remount.
* mprobe: (libc)Heap Consistency Checking.
* mrand48: (libc)SVID Random.
* mrand48_r: (libc)SVID Random.
* mremap: (libc)Memory-mapped I/O.
* msync: (libc)Memory-mapped I/O.
* mtrace: (libc)Tracing malloc.
* munlock: (libc)Page Lock Functions.
* munlockall: (libc)Page Lock Functions.
* munmap: (libc)Memory-mapped I/O.
* muntrace: (libc)Tracing malloc.
* nan: (libc)FP Bit Twiddling.
* nanf: (libc)FP Bit Twiddling.
* nanl: (libc)FP Bit Twiddling.
* nanosleep: (libc)Sleeping.
* nearbyint: (libc)Rounding Functions.
* nearbyintf: (libc)Rounding Functions.
* nearbyintl: (libc)Rounding Functions.
* nextafter: (libc)FP Bit Twiddling.
* nextafterf: (libc)FP Bit Twiddling.
* nextafterl: (libc)FP Bit Twiddling.
* nexttoward: (libc)FP Bit Twiddling.
* nexttowardf: (libc)FP Bit Twiddling.
* nexttowardl: (libc)FP Bit Twiddling.
* nftw64: (libc)Working with Directory Trees.
* nftw: (libc)Working with Directory Trees.
* ngettext: (libc)Advanced gettext functions.
* nice: (libc)Traditional Scheduling Functions.
* nl_langinfo: (libc)The Elegant and Fast Way.
* nrand48: (libc)SVID Random.
* nrand48_r: (libc)SVID Random.
* ntohl: (libc)Byte Order.
* ntohs: (libc)Byte Order.
* ntp_adjtime: (libc)High Accuracy Clock.
* ntp_gettime: (libc)High Accuracy Clock.
* obstack_1grow: (libc)Growing Objects.
* obstack_1grow_fast: (libc)Extra Fast Growing.
* obstack_alignment_mask: (libc)Obstacks Data Alignment.
* obstack_alloc: (libc)Allocation in an Obstack.
* obstack_base: (libc)Status of an Obstack.
* obstack_blank: (libc)Growing Objects.
* obstack_blank_fast: (libc)Extra Fast Growing.
* obstack_chunk_size: (libc)Obstack Chunks.
* obstack_copy0: (libc)Allocation in an Obstack.
* obstack_copy: (libc)Allocation in an Obstack.
* obstack_finish: (libc)Growing Objects.
* obstack_free: (libc)Freeing Obstack Objects.
* obstack_grow0: (libc)Growing Objects.
* obstack_grow: (libc)Growing Objects.
* obstack_init: (libc)Preparing for Obstacks.
* obstack_int_grow: (libc)Growing Objects.
* obstack_int_grow_fast: (libc)Extra Fast Growing.
* obstack_next_free: (libc)Status of an Obstack.
* obstack_object_size: (libc)Growing Objects.
* obstack_object_size: (libc)Status of an Obstack.
* obstack_printf: (libc)Dynamic Output.
* obstack_ptr_grow: (libc)Growing Objects.
* obstack_ptr_grow_fast: (libc)Extra Fast Growing.
* obstack_room: (libc)Extra Fast Growing.
* obstack_vprintf: (libc)Variable Arguments Output.
* offsetof: (libc)Structure Measurement.
* on_exit: (libc)Cleanups on Exit.
* open64: (libc)Opening and Closing Files.
* open: (libc)Opening and Closing Files.
* open_memstream: (libc)String Streams.
* open_obstack_stream: (libc)Obstack Streams.
* opendir: (libc)Opening a Directory.
* openlog: (libc)openlog.
* openpty: (libc)Pseudo-Terminal Pairs.
* parse_printf_format: (libc)Parsing a Template String.
* pathconf: (libc)Pathconf.
* pause: (libc)Using Pause.
* pclose: (libc)Pipe to a Subprocess.
* perror: (libc)Error Messages.
* pipe: (libc)Creating a Pipe.
* popen: (libc)Pipe to a Subprocess.
* posix_memalign: (libc)Aligned Memory Blocks.
* pow10: (libc)Exponents and Logarithms.
* pow10f: (libc)Exponents and Logarithms.
* pow10l: (libc)Exponents and Logarithms.
* pow: (libc)Exponents and Logarithms.
* powf: (libc)Exponents and Logarithms.
* powl: (libc)Exponents and Logarithms.
* pread64: (libc)I/O Primitives.
* pread: (libc)I/O Primitives.
* printf: (libc)Formatted Output Functions.
* printf_size: (libc)Predefined Printf Handlers.
* printf_size_info: (libc)Predefined Printf Handlers.
* psignal: (libc)Signal Messages.
* ptsname: (libc)Allocation.
* ptsname_r: (libc)Allocation.
* putc: (libc)Simple Output.
* putc_unlocked: (libc)Simple Output.
* putchar: (libc)Simple Output.
* putchar_unlocked: (libc)Simple Output.
* putenv: (libc)Environment Access.
* putpwent: (libc)Writing a User Entry.
* puts: (libc)Simple Output.
* pututline: (libc)Manipulating the Database.
* pututxline: (libc)XPG Functions.
* putw: (libc)Simple Output.
* putwc: (libc)Simple Output.
* putwc_unlocked: (libc)Simple Output.
* putwchar: (libc)Simple Output.
* putwchar_unlocked: (libc)Simple Output.
* pwrite64: (libc)I/O Primitives.
* pwrite: (libc)I/O Primitives.
* qecvt: (libc)System V Number Conversion.
* qecvt_r: (libc)System V Number Conversion.
* qfcvt: (libc)System V Number Conversion.
* qfcvt_r: (libc)System V Number Conversion.
* qgcvt: (libc)System V Number Conversion.
* qsort: (libc)Array Sort Function.
* raise: (libc)Signaling Yourself.
* rand: (libc)ISO Random.
* rand_r: (libc)ISO Random.
* random: (libc)BSD Random.
* random_r: (libc)BSD Random.
* rawmemchr: (libc)Search Functions.
* read: (libc)I/O Primitives.
* readdir64: (libc)Reading/Closing Directory.
* readdir64_r: (libc)Reading/Closing Directory.
* readdir: (libc)Reading/Closing Directory.
* readdir_r: (libc)Reading/Closing Directory.
* readlink: (libc)Symbolic Links.
* readv: (libc)Scatter-Gather.
* realloc: (libc)Changing Block Size.
* realpath: (libc)Symbolic Links.
* recv: (libc)Receiving Data.
* recvfrom: (libc)Receiving Datagrams.
* recvmsg: (libc)Receiving Datagrams.
* regcomp: (libc)POSIX Regexp Compilation.
* regerror: (libc)Regexp Cleanup.
* regexec: (libc)Matching POSIX Regexps.
* regfree: (libc)Regexp Cleanup.
* register_printf_function: (libc)Registering New Conversions.
* remainder: (libc)Remainder Functions.
* remainderf: (libc)Remainder Functions.
* remainderl: (libc)Remainder Functions.
* remove: (libc)Deleting Files.
* rename: (libc)Renaming Files.
* rewind: (libc)File Positioning.
* rewinddir: (libc)Random Access Directory.
* rindex: (libc)Search Functions.
* rint: (libc)Rounding Functions.
* rintf: (libc)Rounding Functions.
* rintl: (libc)Rounding Functions.
* rmdir: (libc)Deleting Files.
* round: (libc)Rounding Functions.
* roundf: (libc)Rounding Functions.
* roundl: (libc)Rounding Functions.
* rpmatch: (libc)Yes-or-No Questions.
* sbrk: (libc)Resizing the Data Segment.
* scalb: (libc)Normalization Functions.
* scalbf: (libc)Normalization Functions.
* scalbl: (libc)Normalization Functions.
* scalbln: (libc)Normalization Functions.
* scalblnf: (libc)Normalization Functions.
* scalblnl: (libc)Normalization Functions.
* scalbn: (libc)Normalization Functions.
* scalbnf: (libc)Normalization Functions.
* scalbnl: (libc)Normalization Functions.
* scandir64: (libc)Scanning Directory Content.
* scandir: (libc)Scanning Directory Content.
* scanf: (libc)Formatted Input Functions.
* sched_get_priority_max: (libc)Basic Scheduling Functions.
* sched_get_priority_min: (libc)Basic Scheduling Functions.
* sched_getaffinity: (libc)CPU Affinity.
* sched_getparam: (libc)Basic Scheduling Functions.
* sched_getscheduler: (libc)Basic Scheduling Functions.
* sched_rr_get_interval: (libc)Basic Scheduling Functions.
* sched_setaffinity: (libc)CPU Affinity.
* sched_setparam: (libc)Basic Scheduling Functions.
* sched_setscheduler: (libc)Basic Scheduling Functions.
* sched_yield: (libc)Basic Scheduling Functions.
* seed48: (libc)SVID Random.
* seed48_r: (libc)SVID Random.
* seekdir: (libc)Random Access Directory.
* select: (libc)Waiting for I/O.
* send: (libc)Sending Data.
* sendmsg: (libc)Receiving Datagrams.
* sendto: (libc)Sending Datagrams.
* setbuf: (libc)Controlling Buffering.
* setbuffer: (libc)Controlling Buffering.
* setcontext: (libc)System V contexts.
* setdomainname: (libc)Host Identification.
* setegid: (libc)Setting Groups.
* setenv: (libc)Environment Access.
* seteuid: (libc)Setting User ID.
* setfsent: (libc)fstab.
* setgid: (libc)Setting Groups.
* setgrent: (libc)Scanning All Groups.
* setgroups: (libc)Setting Groups.
* sethostent: (libc)Host Names.
* sethostid: (libc)Host Identification.
* sethostname: (libc)Host Identification.
* setitimer: (libc)Setting an Alarm.
* setjmp: (libc)Non-Local Details.
* setkey: (libc)DES Encryption.
* setkey_r: (libc)DES Encryption.
* setlinebuf: (libc)Controlling Buffering.
* setlocale: (libc)Setting the Locale.
* setlogmask: (libc)setlogmask.
* setmntent: (libc)mtab.
* setnetent: (libc)Networks Database.
* setnetgrent: (libc)Lookup Netgroup.
* setpgid: (libc)Process Group Functions.
* setpgrp: (libc)Process Group Functions.
* setpriority: (libc)Traditional Scheduling Functions.
* setprotoent: (libc)Protocols Database.
* setpwent: (libc)Scanning All Users.
* setregid: (libc)Setting Groups.
* setreuid: (libc)Setting User ID.
* setrlimit64: (libc)Limits on Resources.
* setrlimit: (libc)Limits on Resources.
* setservent: (libc)Services Database.
* setsid: (libc)Process Group Functions.
* setsockopt: (libc)Socket Option Functions.
* setstate: (libc)BSD Random.
* setstate_r: (libc)BSD Random.
* settimeofday: (libc)High-Resolution Calendar.
* setuid: (libc)Setting User ID.
* setutent: (libc)Manipulating the Database.
* setutxent: (libc)XPG Functions.
* setvbuf: (libc)Controlling Buffering.
* shutdown: (libc)Closing a Socket.
* sigaction: (libc)Advanced Signal Handling.
* sigaddset: (libc)Signal Sets.
* sigaltstack: (libc)Signal Stack.
* sigblock: (libc)Blocking in BSD.
* sigdelset: (libc)Signal Sets.
* sigemptyset: (libc)Signal Sets.
* sigfillset: (libc)Signal Sets.
* siginterrupt: (libc)BSD Handler.
* sigismember: (libc)Signal Sets.
* siglongjmp: (libc)Non-Local Exits and Signals.
* sigmask: (libc)Blocking in BSD.
* signal: (libc)Basic Signal Handling.
* signbit: (libc)FP Bit Twiddling.
* significand: (libc)Normalization Functions.
* significandf: (libc)Normalization Functions.
* significandl: (libc)Normalization Functions.
* sigpause: (libc)Blocking in BSD.
* sigpending: (libc)Checking for Pending Signals.
* sigprocmask: (libc)Process Signal Mask.
* sigsetjmp: (libc)Non-Local Exits and Signals.
* sigsetmask: (libc)Blocking in BSD.
* sigstack: (libc)Signal Stack.
* sigsuspend: (libc)Sigsuspend.
* sigvec: (libc)BSD Handler.
* sin: (libc)Trig Functions.
* sincos: (libc)Trig Functions.
* sincosf: (libc)Trig Functions.
* sincosl: (libc)Trig Functions.
* sinf: (libc)Trig Functions.
* sinh: (libc)Hyperbolic Functions.
* sinhf: (libc)Hyperbolic Functions.
* sinhl: (libc)Hyperbolic Functions.
* sinl: (libc)Trig Functions.
* sleep: (libc)Sleeping.
* snprintf: (libc)Formatted Output Functions.
* socket: (libc)Creating a Socket.
* socketpair: (libc)Socket Pairs.
* sprintf: (libc)Formatted Output Functions.
* sqrt: (libc)Exponents and Logarithms.
* sqrtf: (libc)Exponents and Logarithms.
* sqrtl: (libc)Exponents and Logarithms.
* srand48: (libc)SVID Random.
* srand48_r: (libc)SVID Random.
* srand: (libc)ISO Random.
* srandom: (libc)BSD Random.
* srandom_r: (libc)BSD Random.
* sscanf: (libc)Formatted Input Functions.
* ssignal: (libc)Basic Signal Handling.
* stat64: (libc)Reading Attributes.
* stat: (libc)Reading Attributes.
* stime: (libc)Simple Calendar Time.
* stpcpy: (libc)Copying and Concatenation.
* stpncpy: (libc)Copying and Concatenation.
* strcasecmp: (libc)String/Array Comparison.
* strcasestr: (libc)Search Functions.
* strcat: (libc)Copying and Concatenation.
* strchr: (libc)Search Functions.
* strchrnul: (libc)Search Functions.
* strcmp: (libc)String/Array Comparison.
* strcoll: (libc)Collation Functions.
* strcpy: (libc)Copying and Concatenation.
* strcspn: (libc)Search Functions.
* strdup: (libc)Copying and Concatenation.
* strdupa: (libc)Copying and Concatenation.
* strerror: (libc)Error Messages.
* strerror_r: (libc)Error Messages.
* strfmon: (libc)Formatting Numbers.
* strfry: (libc)strfry.
* strftime: (libc)Formatting Calendar Time.
* strlen: (libc)String Length.
* strncasecmp: (libc)String/Array Comparison.
* strncat: (libc)Copying and Concatenation.
* strncmp: (libc)String/Array Comparison.
* strncpy: (libc)Copying and Concatenation.
* strndup: (libc)Copying and Concatenation.
* strndupa: (libc)Copying and Concatenation.
* strnlen: (libc)String Length.
* strpbrk: (libc)Search Functions.
* strptime: (libc)Low-Level Time String Parsing.
* strrchr: (libc)Search Functions.
* strsep: (libc)Finding Tokens in a String.
* strsignal: (libc)Signal Messages.
* strspn: (libc)Search Functions.
* strstr: (libc)Search Functions.
* strtod: (libc)Parsing of Floats.
* strtof: (libc)Parsing of Floats.
* strtoimax: (libc)Parsing of Integers.
* strtok: (libc)Finding Tokens in a String.
* strtok_r: (libc)Finding Tokens in a String.
* strtol: (libc)Parsing of Integers.
* strtold: (libc)Parsing of Floats.
* strtoll: (libc)Parsing of Integers.
* strtoq: (libc)Parsing of Integers.
* strtoul: (libc)Parsing of Integers.
* strtoull: (libc)Parsing of Integers.
* strtoumax: (libc)Parsing of Integers.
* strtouq: (libc)Parsing of Integers.
* strverscmp: (libc)String/Array Comparison.
* strxfrm: (libc)Collation Functions.
* stty: (libc)BSD Terminal Modes.
* swapcontext: (libc)System V contexts.
* swprintf: (libc)Formatted Output Functions.
* swscanf: (libc)Formatted Input Functions.
* symlink: (libc)Symbolic Links.
* sync: (libc)Synchronizing I/O.
* syscall: (libc)System Calls.
* sysconf: (libc)Sysconf Definition.
* sysctl: (libc)System Parameters.
* syslog: (libc)syslog; vsyslog.
* system: (libc)Running a Command.
* sysv_signal: (libc)Basic Signal Handling.
* tan: (libc)Trig Functions.
* tanf: (libc)Trig Functions.
* tanh: (libc)Hyperbolic Functions.
* tanhf: (libc)Hyperbolic Functions.
* tanhl: (libc)Hyperbolic Functions.
* tanl: (libc)Trig Functions.
* tcdrain: (libc)Line Control.
* tcflow: (libc)Line Control.
* tcflush: (libc)Line Control.
* tcgetattr: (libc)Mode Functions.
* tcgetpgrp: (libc)Terminal Access Functions.
* tcgetsid: (libc)Terminal Access Functions.
* tcsendbreak: (libc)Line Control.
* tcsetattr: (libc)Mode Functions.
* tcsetpgrp: (libc)Terminal Access Functions.
* tdelete: (libc)Tree Search Function.
* tdestroy: (libc)Tree Search Function.
* tempnam: (libc)Temporary Files.
* textdomain: (libc)Locating gettext catalog.
* tfind: (libc)Tree Search Function.
* tgamma: (libc)Special Functions.
* tgammaf: (libc)Special Functions.
* tgammal: (libc)Special Functions.
* time: (libc)Simple Calendar Time.
* timegm: (libc)Broken-down Time.
* timelocal: (libc)Broken-down Time.
* times: (libc)Processor Time.
* tmpfile64: (libc)Temporary Files.
* tmpfile: (libc)Temporary Files.
* tmpnam: (libc)Temporary Files.
* tmpnam_r: (libc)Temporary Files.
* toascii: (libc)Case Conversion.
* tolower: (libc)Case Conversion.
* toupper: (libc)Case Conversion.
* towctrans: (libc)Wide Character Case Conversion.
* towlower: (libc)Wide Character Case Conversion.
* towupper: (libc)Wide Character Case Conversion.
* trunc: (libc)Rounding Functions.
* truncate64: (libc)File Size.
* truncate: (libc)File Size.
* truncf: (libc)Rounding Functions.
* truncl: (libc)Rounding Functions.
* tsearch: (libc)Tree Search Function.
* ttyname: (libc)Is It a Terminal.
* ttyname_r: (libc)Is It a Terminal.
* twalk: (libc)Tree Search Function.
* tzset: (libc)Time Zone Functions.
* ulimit: (libc)Limits on Resources.
* umask: (libc)Setting Permissions.
* umount2: (libc)Mount-Unmount-Remount.
* umount: (libc)Mount-Unmount-Remount.
* uname: (libc)Platform Type.
* ungetc: (libc)How Unread.
* ungetwc: (libc)How Unread.
* unlink: (libc)Deleting Files.
* unlockpt: (libc)Allocation.
* unsetenv: (libc)Environment Access.
* updwtmp: (libc)Manipulating the Database.
* utime: (libc)File Times.
* utimes: (libc)File Times.
* utmpname: (libc)Manipulating the Database.
* utmpxname: (libc)XPG Functions.
* va_arg: (libc)Argument Macros.
* va_end: (libc)Argument Macros.
* va_start: (libc)Argument Macros.
* va_start: (libc)Old Varargs.
* valloc: (libc)Aligned Memory Blocks.
* vasprintf: (libc)Variable Arguments Output.
* verr: (libc)Error Messages.
* verrx: (libc)Error Messages.
* versionsort64: (libc)Scanning Directory Content.
* versionsort: (libc)Scanning Directory Content.
* vfork: (libc)Creating a Process.
* vfprintf: (libc)Variable Arguments Output.
* vfscanf: (libc)Variable Arguments Input.
* vfwprintf: (libc)Variable Arguments Output.
* vfwscanf: (libc)Variable Arguments Input.
* vlimit: (libc)Limits on Resources.
* vprintf: (libc)Variable Arguments Output.
* vscanf: (libc)Variable Arguments Input.
* vsnprintf: (libc)Variable Arguments Output.
* vsprintf: (libc)Variable Arguments Output.
* vsscanf: (libc)Variable Arguments Input.
* vswprintf: (libc)Variable Arguments Output.
* vswscanf: (libc)Variable Arguments Input.
* vsyslog: (libc)syslog; vsyslog.
* vtimes: (libc)Resource Usage.
* vwarn: (libc)Error Messages.
* vwarnx: (libc)Error Messages.
* vwprintf: (libc)Variable Arguments Output.
* vwscanf: (libc)Variable Arguments Input.
* wait3: (libc)BSD Wait Functions.
* wait4: (libc)Process Completion.
* wait: (libc)Process Completion.
* waitpid: (libc)Process Completion.
* warn: (libc)Error Messages.
* warnx: (libc)Error Messages.
* wcpcpy: (libc)Copying and Concatenation.
* wcpncpy: (libc)Copying and Concatenation.
* wcrtomb: (libc)Converting a Character.
* wcscasecmp: (libc)String/Array Comparison.
* wcscat: (libc)Copying and Concatenation.
* wcschr: (libc)Search Functions.
* wcschrnul: (libc)Search Functions.
* wcscmp: (libc)String/Array Comparison.
* wcscoll: (libc)Collation Functions.
* wcscpy: (libc)Copying and Concatenation.
* wcscspn: (libc)Search Functions.
* wcsdup: (libc)Copying and Concatenation.
* wcsftime: (libc)Formatting Calendar Time.
* wcslen: (libc)String Length.
* wcsncasecmp: (libc)String/Array Comparison.
* wcsncat: (libc)Copying and Concatenation.
* wcsncmp: (libc)String/Array Comparison.
* wcsncpy: (libc)Copying and Concatenation.
* wcsnlen: (libc)String Length.
* wcsnrtombs: (libc)Converting Strings.
* wcspbrk: (libc)Search Functions.
* wcsrchr: (libc)Search Functions.
* wcsrtombs: (libc)Converting Strings.
* wcsspn: (libc)Search Functions.
* wcsstr: (libc)Search Functions.
* wcstod: (libc)Parsing of Floats.
* wcstof: (libc)Parsing of Floats.
* wcstoimax: (libc)Parsing of Integers.
* wcstok: (libc)Finding Tokens in a String.
* wcstol: (libc)Parsing of Integers.
* wcstold: (libc)Parsing of Floats.
* wcstoll: (libc)Parsing of Integers.
* wcstombs: (libc)Non-reentrant String Conversion.
* wcstoq: (libc)Parsing of Integers.
* wcstoul: (libc)Parsing of Integers.
* wcstoull: (libc)Parsing of Integers.
* wcstoumax: (libc)Parsing of Integers.
* wcstouq: (libc)Parsing of Integers.
* wcswcs: (libc)Search Functions.
* wcsxfrm: (libc)Collation Functions.
* wctob: (libc)Converting a Character.
* wctomb: (libc)Non-reentrant Character Conversion.
* wctrans: (libc)Wide Character Case Conversion.
* wctype: (libc)Classification of Wide Characters.
* wmemchr: (libc)Search Functions.
* wmemcmp: (libc)String/Array Comparison.
* wmemcpy: (libc)Copying and Concatenation.
* wmemmove: (libc)Copying and Concatenation.
* wmempcpy: (libc)Copying and Concatenation.
* wmemset: (libc)Copying and Concatenation.
* wordexp: (libc)Calling Wordexp.
* wordfree: (libc)Calling Wordexp.
* wprintf: (libc)Formatted Output Functions.
* write: (libc)I/O Primitives.
* writev: (libc)Scatter-Gather.
* wscanf: (libc)Formatted Input Functions.
* y0: (libc)Special Functions.
* y0f: (libc)Special Functions.
* y0l: (libc)Special Functions.
* y1: (libc)Special Functions.
* y1f: (libc)Special Functions.
* y1l: (libc)Special Functions.
* yn: (libc)Special Functions.
* ynf: (libc)Special Functions.
* ynl: (libc)Special Functions.
END-INFO-DIR-ENTRY

   This file documents the GNU C library.

   This is Edition 0.10, last updated 2001-07-06, of `The GNU C Library
Reference Manual', for Version 2.3.x.

   Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2001, 2002,
2003 Free Software Foundation, Inc.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.1 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "Free Software Needs Free Documentation" and
"GNU Lesser General Public License", the Front-Cover texts being (a)
(see below), and with the Back-Cover Texts being (b) (see below).  A
copy of the license is included in the section entitled "GNU Free
Documentation License".

   (a) The FSF's Front-Cover Text is:

   A GNU Manual

   (b) The FSF's Back-Cover Text is:

   You have freedom to copy and modify this GNU Manual, like GNU
software.  Copies published by the Free Software Foundation raise
funds for GNU development.


File: libc.info,  Node: Errors in Math Functions,  Next: Pseudo-Random Numbers,  Prev: Special Functions,  Up: Mathematics

19.7 Known Maximum Errors in Math Functions
===========================================

This section lists the known errors of the functions in the math
library.  Errors are measured in "units of the last place".  This is a
measure for the relative error.  For a number z with the representation
d.d...d*2^e (we assume IEEE floating-point numbers with base 2) the ULP
is represented by

     |d.d...d - (z / 2^e)| / 2^(p - 1)

where p is the number of bits in the mantissa of the floating-point
number representation.  Ideally the error for all functions is always
less than 0.5ulps.  Using rounding bits this is also possible and
normally implemented for the basic operations.  To achieve the same for
the complex math functions requires a lot more work and this has not
yet been done.

   Therefore many of the functions in the math library have errors.  The
table lists the maximum error for each function which is exposed by one
of the existing tests in the test suite.  The table tries to cover as
much as possible and list the actual maximum error (or at least a
ballpark figure) but this is often not achieved due to the large search
space.

   The table lists the ULP values for different architectures.
Different architectures have different results since their hardware
support for floating-point operations varies and also the existing
hardware support is different.

Function      Alpha           ARM             Generic         hppa/fpu        ix86
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               622
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               -               -               -               -
asinf         -               2               -               -               -
asin          -               1               -               -               -
asinl         -               -               -               -               1
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               -               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        1               -               -               1               -
atanh         -               1               -               -               -
atanhl        -               -               -               -               1
atan2f        6               -               -               3               -
atan2         -               -               -               -               -
atan2l        -               -               -               -               -
cabsf         -               1               -               -               -
cabs          -               1               -               -               -
cabsl         -               -               -               -               -
cacosf        -               1 + i 1         -               -               0 + i 1
cacos         -               1 + i 0         -               -               -
cacosl        -               -               -               -               0 + i 2
cacoshf       7 + i 3         7 + i 3         -               7 + i 3         9 + i 4
cacosh        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
cacoshl       -               -               -               -               6 + i 1
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 0         2 + i 1         -               1 + i 0         1 + i 1
casin         1 + i 0         3 + i 0         -               1 + i 0         1 + i 0
casinl        -               -               -               -               2 + i 2
casinhf       1 + i 6         1 + i 6         -               1 + i 6         1 + i 6
casinh        5 + i 3         5 + i 3         -               5 + i 3         5 + i 3
casinhl       -               -               -               -               5 + i 5
catanf        4 + i 1         4 + i 1         -               4 + i 1         0 + i 1
catan         0 + i 1         0 + i 1         -               0 + i 1         0 + i 1
catanl        -               -               -               -               -
catanhf       0 + i 6         1 + i 6         -               0 + i 6         1 + i 0
catanh        4 + i 0         4 + i 1         -               4 + i 0         2 + i 0
catanhl       -               -               -               -               1 + i 0
cbrtf         -               -               -               -               -
cbrt          1               1               -               1               -
cbrtl         -               -               -               -               1
ccosf         1 + i 1         0 + i 1         -               1 + i 1         0 + i 1
ccos          1 + i 0         1 + i 1         -               1 + i 0         1 + i 0
ccosl         -               -               -               -               1 + i 1
ccoshf        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
ccosh         1 + i 0         1 + i 1         -               1 + i 0         1 + i 1
ccoshl        -               -               -               -               0 + i 1
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         1 + i 1         -               1 + i 1         -
cexp          -               1 + i 0         -               -               -
cexpl         -               -               -               -               1 + i 1
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 3         0 + i 3         -               1 + i 3         1 + i 0
clog          -               0 + i 1         -               -               -
clogl         -               -               -               -               1 + i 0
clog10f       1 + i 5         1 + i 5         -               1 + i 5         1 + i 1
clog10        0 + i 1         1 + i 1         -               0 + i 1         1 + i 1
clog10l       -               -               -               -               1 + i 1
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               -               1               1
cos           2               2               -               2               2
cosl          -               -               -               -               1
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         4 + i 2         4 + i 2         -               4 + i 2         4 + i 3
cpow          2 + i 2         1 + i 1.1031    -               2 + i 2         1 + i 2
cpowl         -               -               -               -               763 + i 2
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         -               0 + i 1         -               -               1 + i 1
csin          -               -               -               -               -
csinl         -               -               -               -               1 + i 0
csinhf        1 + i 1         1 + i 1         -               1 + i 1         1 + i 1
csinh         0 + i 1         0 + i 1         -               0 + i 1         1 + i 1
csinhl        -               -               -               -               1 + i 2
csqrtf        1 + i 0         1 + i 1         -               1 + i 0         -
csqrt         -               1 + i 0         -               -               -
csqrtl        -               -               -               -               -
ctanf         -               1 + i 1         -               -               0 + i 1
ctan          0 + i 1         1 + i 1         -               1 + i 1         1 + i 1
ctanl         -               -               -               -               439 + i 3
ctanhf        2 + i 1         2 + i 1         -               2 + i 1         1 + i 1
ctanh         1 + i 0         2 + i 2         -               1 + i 0         0 + i 1
ctanhl        -               -               -               -               5 + i 25
erff          -               -               -               -               -
erf           1               -               -               1               1
erfl          -               -               -               -               -
erfcf         -               12              -               -               1
erfc          1               24              -               1               1
erfcl         -               -               -               -               1
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               2               -               2               -
exp10         6               6               -               6               -
exp10l        -               -               -               -               8
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        1               1               -               1               -
expm1         1               -               -               1               -
expm1l        -               -               -               -               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               1               -               -               -
fmod          -               2               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               1
gammal        -               -               -               -               1
hypotf        1               1               -               1               1
hypot         -               1               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           2               2               -               2               1
j0            2               2               -               2               1
j0l           -               -               -               -               1
j1f           2               2               -               2               1
j1            1               1               -               1               1
j1l           -               -               -               -               1
jnf           4               4               -               4               2
jn            4               6               -               4               2
jnl           -               -               -               -               2
lgammaf       2               2               -               2               2
lgamma        1               1               -               1               1
lgammal       -               -               -               -               1
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          -               1               -               -               1
log           -               1               -               -               -
logl          -               -               -               -               -
log10f        2               1               -               2               1
log10         1               1               -               1               -
log10l        -               -               -               -               1
log1pf        1               1               -               1               -
log1p         -               1               -               -               -
log1pl        -               -               -               -               -
log2f         -               1               -               -               -
log2          -               1               -               -               -
log2l         -               -               -               -               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               -               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               -               1               1
sincos        1               1               -               1               1
sincosl       -               -               -               -               1
sinhf         -               1               -               -               -
sinh          -               1               -               -               -
sinhl         -               -               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               -               -
tanf          -               -               -               -               -
tan           1               0.5             -               1               1
tanl          -               -               -               -               -
tanhf         -               1               -               -               -
tanh          -               1               -               -               -
tanhl         -               -               -               -               -
tgammaf       1               1               -               1               1
tgamma        1               1               -               1               2
tgammal       -               -               -               -               1
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               -               1               1
y0            2               2               -               2               2
y0l           -               -               -               -               1
y1f           2               2               -               2               2
y1            3               3               -               3               2
y1l           -               -               -               -               1
ynf           2               2               -               2               3
yn            3               3               -               3               2
ynl           -               -               -               -               4

Function      IA64            M68k            MIPS            PowerPC         powerpc/nofpu
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               -
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               1               -               -               -
asinf         -               -               -               -               -
asin          -               -               -               -               -
asinl         -               -               -               -               -
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               1               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        -               -               1               1               1
atanh         -               -               -               -               -
atanhl        -               1               -               -               -
atan2f        -               -               3               6               3
atan2         -               -               -               -               -
atan2l        -               1               -               -               -
cabsf         -               -               -               -               -
cabs          -               -               -               -               -
cabsl         -               -               -               -               -
cacosf        0 + i 1         2 + i 1         -               -               -
cacos         -               -               -               -               -
cacosl        0 + i 2         1 + i 2         -               -               -
cacoshf       7 + i 0         7 + i 1         7 + i 3         7 + i 3         7 + i 3
cacosh        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cacoshl       7 + i 1         6 + i 2         -               -               -
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 1         5 + i 1         1 + i 0         1 + i 0         1 + i 0
casin         1 + i 0         1 + i 0         1 + i 0         1 + i 0         1 + i 0
casinl        2 + i 2         3 + i 2         -               -               -
casinhf       1 + i 6         19 + i 1        1 + i 6         1 + i 6         1 + i 6
casinh        5 + i 3         6 + i 13        5 + i 3         5 + i 3         5 + i 3
casinhl       5 + i 5         5 + i 6         -               -               -
catanf        0 + i 1         0 + i 1         4 + i 1         4 + i 1         4 + i 1
catan         0 + i 1         0 + i 1         0 + i 1         0 + i 1         0 + i 1
catanl        -               1 + i 0         -               -               -
catanhf       -               -               0 + i 6         0 + i 6         0 + i 6
catanh        4 + i 0         -               4 + i 0         4 + i 0         4 + i 0
catanhl       1 + i 0         1 + i 0         -               -               -
cbrtf         -               -               -               -               -
cbrt          -               -               1               1               1
cbrtl         -               1               -               -               -
ccosf         0 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccos          1 + i 0         -               1 + i 0         1 + i 0         1 + i 0
ccosl         1 + i 1         1 + i 1         -               -               -
ccoshf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccosh         1 + i 1         -               1 + i 0         1 + i 0         1 + i 0
ccoshl        0 + i 1         0 + i 1         -               -               -
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         2 + i 1         1 + i 1         1 + i 1         1 + i 1
cexp          -               -               -               -               -
cexpl         0 + i 1         0 + i 1         -               -               -
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 0         1 + i 0         1 + i 3         1 + i 3         1 + i 3
clog          -               -               -               -               -
clogl         1 + i 0         1 + i 1         -               -               -
clog10f       1 + i 1         1 + i 1         1 + i 5         1 + i 5         1 + i 5
clog10        1 + i 1         1 + i 1         0 + i 1         0 + i 1         0 + i 1
clog10l       1 + i 1         1 + i 2         -               -               -
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               1               1               1
cos           2               2               2               2               2
cosl          1               1               -               -               -
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         5 + i 3         2 + i 6         4 + i 2         4 + i 2         4 + i 2
cpow          2 + i 2         1 + i 2         2 + i 2         2 + i 2         2 + i 2
cpowl         3 + i 4         15 + i 2        -               -               -
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         1 + i 1         1 + i 1         -               -               -
csin          -               -               -               -               -
csinl         1 + i 0         1 + i 0         -               -               -
csinhf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
csinh         1 + i 1         -               0 + i 1         0 + i 1         0 + i 1
csinhl        1 + i 2         1 + i 0         -               -               -
csqrtf        1 + i 0         -               1 + i 0         1 + i 0         1 + i 0
csqrt         -               -               -               -               -
csqrtl        -               -               -               -               -
ctanf         0 + i 1         -               -               -               -
ctan          1 + i 1         1 + i 0         1 + i 1         1 + i 1         1 + i 1
ctanl         2 + i 1         1 + i 2         -               -               -
ctanhf        0 + i 1         0 + i 1         2 + i 1         2 + i 1         2 + i 1
ctanh         1 + i 1         0 + i 1         1 + i 0         1 + i 0         1 + i 0
ctanhl        1 + i 24        0 + i 1         -               -               -
erff          -               -               -               -               -
erf           1               -               1               1               1
erfl          -               -               -               -               -
erfcf         1               1               -               1               -
erfc          1               -               1               1               1
erfcl         1               1               -               -               -
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               -               2               2               2
exp10         6               -               6               6               6
exp10l        3               -               -               -               -
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        -               -               1               1               1
expm1         -               -               1               1               1
expm1l        1               1               -               -               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               -               -               -               -
fmod          -               -               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               -
gammal        1               1               -               -               -
hypotf        1               1               1               1               1
hypot         -               -               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           1               1               2               1               2
j0            2               1               2               2               2
j0l           2               1               -               -               -
j1f           2               2               2               2               2
j1            1               -               1               1               1
j1l           1               1               -               -               -
jnf           3               5               4               3               4
jn            3               1               4               3               4
jnl           2               2               -               -               -
lgammaf       2               2               2               2               2
lgamma        1               1               1               1               1
lgammal       1               1               -               -               -
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          1               1               -               -               -
log           -               -               -               -               -
logl          -               1               -               -               -
log10f        1               1               2               2               2
log10         -               -               1               1               1
log10l        1               2               -               -               -
log1pf        -               -               1               1               1
log1p         -               -               -               -               -
log1pl        -               1               -               -               -
log2f         -               -               -               -               -
log2          -               -               -               -               -
log2l         -               1               -               -               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               1               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               1               1               1
sincos        1               1               1               1               1
sincosl       1               1               -               -               -
sinhf         -               -               -               -               -
sinh          -               -               -               -               -
sinhl         -               1               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               -               -
tanf          -               -               -               -               -
tan           1               1               1               1               1
tanl          -               1               -               -               -
tanhf         -               -               -               -               -
tanh          -               -               -               -               -
tanhl         -               -               -               -               -
tgammaf       1               1               1               1               1
tgamma        1               1               1               1               1
tgammal       1               1               -               -               -
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               1               1               1
y0            2               1               2               2               2
y0l           1               2               -               -               -
y1f           2               2               2               2               2
y1            3               1               3               3               3
y1l           1               1               -               -               -
ynf           2               2               2               2               2
yn            3               1               3               3               3
ynl           2               4               -               -               -

Function      S/390           SH4             Sparc 32-bit    Sparc 64-bit    x86_64/fpu
acosf         -               -               -               -               -
acos          -               -               -               -               -
acosl         -               -               -               -               1
acoshf        -               -               -               -               -
acosh         -               -               -               -               -
acoshl        -               -               -               -               -
asinf         -               2               -               -               -
asin          -               1               -               -               -
asinl         -               -               -               -               1
asinhf        -               -               -               -               -
asinh         -               -               -               -               -
asinhl        -               -               -               -               -
atanf         -               -               -               -               -
atan          -               -               -               -               -
atanl         -               -               -               -               -
atanhf        1               -               1               1               1
atanh         -               1               -               -               -
atanhl        -               -               -               -               1
atan2f        6               4               6               6               6
atan2         -               -               -               -               -
atan2l        -               -               -               1               -
cabsf         -               1               -               -               -
cabs          -               1               -               -               -
cabsl         -               -               -               -               -
cacosf        -               1 + i 1         -               -               0 + i 1
cacos         -               1 + i 0         -               -               -
cacosl        -               -               -               0 + i 1         0 + i 2
cacoshf       7 + i 3         7 + i 3         7 + i 3         7 + i 3         7 + i 3
cacosh        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cacoshl       -               -               -               5 + i 1         6 + i 1
cargf         -               -               -               -               -
carg          -               -               -               -               -
cargl         -               -               -               -               -
casinf        1 + i 0         2 + i 1         1 + i 0         1 + i 0         1 + i 1
casin         1 + i 0         3 + i 0         1 + i 0         1 + i 0         1 + i 0
casinl        -               -               -               0 + i 1         2 + i 2
casinhf       1 + i 6         1 + i 6         1 + i 6         1 + i 6         1 + i 6
casinh        5 + i 3         5 + i 3         5 + i 3         5 + i 3         5 + i 3
casinhl       -               -               -               4 + i 2         5 + i 5
catanf        4 + i 1         4 + i 1         4 + i 1         4 + i 1         4 + i 1
catan         0 + i 1         0 + i 1         0 + i 1         0 + i 1         0 + i 1
catanl        -               -               -               0 + i 1         -
catanhf       0 + i 6         1 + i 6         0 + i 6         0 + i 6         0 + i 6
catanh        4 + i 0         4 + i 1         4 + i 0         4 + i 0         4 + i 0
catanhl       -               -               -               1 + i 1         1 + i 0
cbrtf         -               -               -               -               -
cbrt          1               1               1               1               1
cbrtl         -               -               -               1               1
ccosf         1 + i 1         0 + i 1         1 + i 1         1 + i 1         1 + i 1
ccos          1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 0
ccosl         -               -               -               1 + i 1         1 + i 1
ccoshf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ccosh         1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 1
ccoshl        -               -               -               1 + i 1         0 + i 1
ceilf         -               -               -               -               -
ceil          -               -               -               -               -
ceill         -               -               -               -               -
cexpf         1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
cexp          -               1 + i 0         -               -               -
cexpl         -               -               -               1 + i 1         0 + i 1
cimagf        -               -               -               -               -
cimag         -               -               -               -               -
cimagl        -               -               -               -               -
clogf         1 + i 3         0 + i 3         1 + i 3         1 + i 3         1 + i 3
clog          -               0 + i 1         -               -               -
clogl         -               -               -               1 + i 0         1 + i 0
clog10f       1 + i 5         1 + i 5         1 + i 5         1 + i 5         1 + i 5
clog10        0 + i 1         1 + i 1         0 + i 1         0 + i 1         1 + i 1
clog10l       -               -               -               1 + i 1         1 + i 1
conjf         -               -               -               -               -
conj          -               -               -               -               -
conjl         -               -               -               -               -
copysignf     -               -               -               -               -
copysign      -               -               -               -               -
copysignl     -               -               -               -               -
cosf          1               1               1               1               1
cos           2               2               2               2               2
cosl          -               -               -               1               1
coshf         -               -               -               -               -
cosh          -               -               -               -               -
coshl         -               -               -               -               -
cpowf         4 + i 2         4 + i 2         4 + i 2         4 + i 2         5 + i 2
cpow          2 + i 2         1 + i 1.1031    2 + i 2         2 + i 2         2 + i 2
cpowl         -               -               -               10 + i 1        5 + i 2
cprojf        -               -               -               -               -
cproj         -               -               -               -               -
cprojl        -               -               -               -               -
crealf        -               -               -               -               -
creal         -               -               -               -               -
creall        -               -               -               -               -
csinf         -               0 + i 1         -               -               0 + i 1
csin          -               -               -               -               0 + i 1
csinl         -               -               -               1 + i 1         1 + i 0
csinhf        1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
csinh         0 + i 1         0 + i 1         0 + i 1         0 + i 1         1 + i 1
csinhl        -               -               -               1 + i 0         1 + i 2
csqrtf        1 + i 0         1 + i 1         1 + i 0         1 + i 0         1 + i 0
csqrt         -               1 + i 0         -               -               -
csqrtl        -               -               -               1 + i 1         -
ctanf         -               1 + i 1         -               -               0 + i 1
ctan          1 + i 1         1 + i 1         1 + i 1         1 + i 1         1 + i 1
ctanl         -               -               -               1 + i 2         439 + i 3
ctanhf        2 + i 1         2 + i 1         2 + i 1         2 + i 1         2 + i 1
ctanh         1 + i 0         2 + i 2         1 + i 0         1 + i 0         1 + i 1
ctanhl        -               -               -               1 + i 1         5 + i 25
erff          -               -               -               -               -
erf           1               -               1               1               1
erfl          -               -               -               -               -
erfcf         1               12              -               -               -
erfc          1               24              1               1               1
erfcl         -               -               -               1               1
expf          -               -               -               -               -
exp           -               -               -               -               -
expl          -               -               -               -               -
exp10f        2               2               2               2               2
exp10         6               6               6               6               6
exp10l        -               -               -               1               8
exp2f         -               -               -               -               -
exp2          -               -               -               -               -
exp2l         -               -               -               -               -
expm1f        1               1               1               1               1
expm1         1               -               1               1               1
expm1l        -               -               -               1               -
fabsf         -               -               -               -               -
fabs          -               -               -               -               -
fabsl         -               -               -               -               -
fdimf         -               -               -               -               -
fdim          -               -               -               -               -
fdiml         -               -               -               -               -
floorf        -               -               -               -               -
floor         -               -               -               -               -
floorl        -               -               -               -               -
fmaf          -               -               -               -               -
fma           -               -               -               -               -
fmal          -               -               -               -               -
fmaxf         -               -               -               -               -
fmax          -               -               -               -               -
fmaxl         -               -               -               -               -
fminf         -               -               -               -               -
fmin          -               -               -               -               -
fminl         -               -               -               -               -
fmodf         -               1               -               -               -
fmod          -               2               -               -               -
fmodl         -               -               -               -               -
frexpf        -               -               -               -               -
frexp         -               -               -               -               -
frexpl        -               -               -               -               -
gammaf        -               -               -               -               -
gamma         -               -               -               -               -
gammal        -               -               -               1               1
hypotf        1               1               1               1               1
hypot         -               1               -               -               -
hypotl        -               -               -               -               -
ilogbf        -               -               -               -               -
ilogb         -               -               -               -               -
ilogbl        -               -               -               -               -
j0f           2               2               2               2               2
j0            2               2               2               2               2
j0l           -               -               -               2               1
j1f           2               2               2               2               2
j1            1               1               1               1               1
j1l           -               -               -               4               1
jnf           4               4               4               4               4
jn            4               6               4               4               4
jnl           -               -               -               4               2
lgammaf       2               2               2               2               2
lgamma        1               1               1               1               1
lgammal       -               -               -               1               1
lrintf        -               -               -               -               -
lrint         -               -               -               -               -
lrintl        -               -               -               -               -
llrintf       -               -               -               -               -
llrint        -               -               -               -               -
llrintl       -               -               -               -               -
logf          -               1               -               -               -
log           -               1               -               -               -
logl          -               -               -               -               -
log10f        2               1               2               2               2
log10         1               1               1               1               1
log10l        -               -               -               1               1
log1pf        1               1               1               1               1
log1p         -               1               -               -               -
log1pl        -               -               -               1               -
log2f         -               1               -               -               -
log2          -               1               -               -               -
log2l         -               -               -               1               -
logbf         -               -               -               -               -
logb          -               -               -               -               -
logbl         -               -               -               -               -
lroundf       -               -               -               -               -
lround        -               -               -               -               -
lroundl       -               -               -               -               -
llroundf      -               -               -               -               -
llround       -               -               -               -               -
llroundl      -               -               -               -               -
modff         -               -               -               -               -
modf          -               -               -               -               -
modfl         -               -               -               -               -
nearbyintf    -               -               -               -               -
nearbyint     -               -               -               -               -
nearbyintl    -               -               -               -               -
nextafterf    -               -               -               -               -
nextafter     -               -               -               -               -
nextafterl    -               -               -               -               -
nexttowardf   -               -               -               -               -
nexttoward    -               -               -               -               -
nexttowardl   -               -               -               -               -
powf          -               -               -               -               -
pow           -               -               -               -               -
powl          -               -               -               -               -
remainderf    -               -               -               -               -
remainder     -               -               -               -               -
remainderl    -               -               -               -               -
remquof       -               -               -               -               -
remquo        -               -               -               -               -
remquol       -               -               -               -               -
rintf         -               -               -               -               -
rint          -               -               -               -               -
rintl         -               -               -               -               -
roundf        -               -               -               -               -
round         -               -               -               -               -
roundl        -               -               -               -               -
scalbf        -               -               -               -               -
scalb         -               -               -               -               -
scalbl        -               -               -               -               -
scalbnf       -               -               -               -               -
scalbn        -               -               -               -               -
scalbnl       -               -               -               -               -
scalblnf      -               -               -               -               -
scalbln       -               -               -               -               -
scalblnl      -               -               -               -               -
sinf          -               -               -               -               -
sin           -               -               -               -               -
sinl          -               -               -               -               -
sincosf       1               1               1               1               1
sincos        1               1               1               1               1
sincosl       -               -               -               1               1
sinhf         -               1               -               -               -
sinh          -               1               -               -               -
sinhl         -               -               -               -               -
sqrtf         -               -               -               -               -
sqrt          -               -               -               -               -
sqrtl         -               -               -               1               -
tanf          -               -               -               -               -
tan           1               0.5             1               1               1
tanl          -               -               -               -               -
tanhf         -               1               -               -               -
tanh          -               1               -               -               -
tanhl         -               -               -               1               -
tgammaf       1               1               1               1               1
tgamma        1               1               1               1               1
tgammal       -               -               -               1               1
truncf        -               -               -               -               -
trunc         -               -               -               -               -
truncl        -               -               -               -               -
y0f           1               1               1               1               1
y0            2               2               2               2               2
y0l           -               -               -               3               1
y1f           2               2               2               2               2
y1            3               3               3               3               3
y1l           -               -               -               1               1
ynf           2               2               2               2               2
yn            3               3               3               3               3
ynl           -               -               -               5               4


File: libc.info,  Node: Pseudo-Random Numbers,  Next: FP Function Optimizations,  Prev: Errors in Math Functions,  Up: Mathematics

19.8 Pseudo-Random Numbers
==========================

This section describes the GNU facilities for generating a series of
pseudo-random numbers.  The numbers generated are not truly random;
typically, they form a sequence that repeats periodically, with a period
so large that you can ignore it for ordinary purposes.  The random
number generator works by remembering a "seed" value which it uses to
compute the next random number and also to compute a new seed.

   Although the generated numbers look unpredictable within one run of a
program, the sequence of numbers is _exactly the same_ from one run to
the next.  This is because the initial seed is always the same.  This
is convenient when you are debugging a program, but it is unhelpful if
you want the program to behave unpredictably.  If you want a different
pseudo-random series each time your program runs, you must specify a
different seed each time.  For ordinary purposes, basing the seed on the
current time works well.

   You can obtain repeatable sequences of numbers on a particular
machine type by specifying the same initial seed value for the random
number generator.  There is no standard meaning for a particular seed
value; the same seed, used in different C libraries or on different CPU
types, will give you different random numbers.

   The GNU library supports the standard ISO C random number functions
plus two other sets derived from BSD and SVID.  The BSD and ISO C
functions provide identical, somewhat limited functionality.  If only a
small number of random bits are required, we recommend you use the
ISO C interface, `rand' and `srand'.  The SVID functions provide a more
flexible interface, which allows better random number generator
algorithms, provides more random bits (up to 48) per call, and can
provide random floating-point numbers.  These functions are required by
the XPG standard and therefore will be present in all modern Unix
systems.

* Menu:

* ISO Random::                  `rand' and friends.
* BSD Random::                  `random' and friends.
* SVID Random::                 `drand48' and friends.


File: libc.info,  Node: ISO Random,  Next: BSD Random,  Up: Pseudo-Random Numbers

19.8.1 ISO C Random Number Functions
------------------------------------

This section describes the random number functions that are part of the
ISO C standard.

   To use these facilities, you should include the header file
`stdlib.h' in your program.  

 -- Macro: int RAND_MAX
     The value of this macro is an integer constant representing the
     largest value the `rand' function can return.  In the GNU library,
     it is `2147483647', which is the largest signed integer
     representable in 32 bits.  In other libraries, it may be as low as
     `32767'.

 -- Function: int rand (void)
     The `rand' function returns the next pseudo-random number in the
     series.  The value ranges from `0' to `RAND_MAX'.

 -- Function: void srand (unsigned int SEED)
     This function establishes SEED as the seed for a new series of
     pseudo-random numbers.  If you call `rand' before a seed has been
     established with `srand', it uses the value `1' as a default seed.

     To produce a different pseudo-random series each time your program
     is run, do `srand (time (0))'.

   POSIX.1 extended the C standard functions to support reproducible
random numbers in multi-threaded programs.  However, the extension is
badly designed and unsuitable for serious work.

 -- Function: int rand_r (unsigned int *SEED)
     This function returns a random number in the range 0 to `RAND_MAX'
     just as `rand' does.  However, all its state is stored in the SEED
     argument.  This means the RNG's state can only have as many bits
     as the type `unsigned int' has.  This is far too few to provide a
     good RNG.

     If your program requires a reentrant RNG, we recommend you use the
     reentrant GNU extensions to the SVID random number generator.  The
     POSIX.1 interface should only be used when the GNU extensions are
     not available.


File: libc.info,  Node: BSD Random,  Next: SVID Random,  Prev: ISO Random,  Up: Pseudo-Random Numbers

19.8.2 BSD Random Number Functions
----------------------------------

This section describes a set of random number generation functions that
are derived from BSD.  There is no advantage to using these functions
with the GNU C library; we support them for BSD compatibility only.

   The prototypes for these functions are in `stdlib.h'.  

 -- Function: long int random (void)
     This function returns the next pseudo-random number in the
     sequence.  The value returned ranges from `0' to `RAND_MAX'.

     *Note_* Temporarily this function was defined to return a
     `int32_t' value to indicate that the return value always contains
     32 bits even if `long int' is wider.  The standard demands it
     differently.  Users must always be aware of the 32-bit limitation,
     though.

 -- Function: void srandom (unsigned int SEED)
     The `srandom' function sets the state of the random number
     generator based on the integer SEED.  If you supply a SEED value
     of `1', this will cause `random' to reproduce the default set of
     random numbers.

     To produce a different set of pseudo-random numbers each time your
     program runs, do `srandom (time (0))'.

 -- Function: void * initstate (unsigned int SEED, void *STATE, size_t
          SIZE)
     The `initstate' function is used to initialize the random number
     generator state.  The argument STATE is an array of SIZE bytes,
     used to hold the state information.  It is initialized based on
     SEED.  The size must be between 8 and 256 bytes, and should be a
     power of two.  The bigger the STATE array, the better.

     The return value is the previous value of the state information
     array.  You can use this value later as an argument to `setstate'
     to restore that state.

 -- Function: void * setstate (void *STATE)
     The `setstate' function restores the random number state
     information STATE.  The argument must have been the result of a
     previous call to INITSTATE or SETSTATE.

     The return value is the previous value of the state information
     array.  You can use this value later as an argument to `setstate'
     to restore that state.

     If the function fails the return value is `NULL'.

   The four functions described so far in this section all work on a
state which is shared by all threads.  The state is not directly
accessible to the user and can only be modified by these functions.
This makes it hard to deal with situations where each thread should
have its own pseudo-random number generator.

   The GNU C library contains four additional functions which contain
the state as an explicit parameter and therefore make it possible to
handle thread-local PRNGs.  Beside this there are no difference.  In
fact, the four functions already discussed are implemented internally
using the following interfaces.

   The `stdlib.h' header contains a definition of the following type:

 -- Data Type: struct random_data
     Objects of type `struct random_data' contain the information
     necessary to represent the state of the PRNG.  Although a complete
     definition of the type is present the type should be treated as
     opaque.

   The functions modifying the state follow exactly the already
described functions.

 -- Function: int random_r (struct random_data *restrict BUF, int32_t
          *restrict RESULT)
     The `random_r' function behaves exactly like the `random' function
     except that it uses and modifies the state in the object pointed
     to by the first parameter instead of the global state.

 -- Function: int srandom_r (unsigned int SEED, struct random_data *BUF)
     The `srandom_r' function behaves exactly like the `srandom'
     function except that it uses and modifies the state in the object
     pointed to by the second parameter instead of the global state.

 -- Function: int initstate_r (unsigned int SEED, char *restrict
          STATEBUF, size_t STATELEN, struct random_data *restrict BUF)
     The `initstate_r' function behaves exactly like the `initstate'
     function except that it uses and modifies the state in the object
     pointed to by the fourth parameter instead of the global state.

 -- Function: int setstate_r (char *restrict STATEBUF, struct
          random_data *restrict BUF)
     The `setstate_r' function behaves exactly like the `setstate'
     function except that it uses and modifies the state in the object
     pointed to by the first parameter instead of the global state.


File: libc.info,  Node: SVID Random,  Prev: BSD Random,  Up: Pseudo-Random Numbers

19.8.3 SVID Random Number Function
----------------------------------

The C library on SVID systems contains yet another kind of random number
generator functions.  They use a state of 48 bits of data.  The user can
choose among a collection of functions which return the random bits in
different forms.

   Generally there are two kinds of function.  The first uses a state of
the random number generator which is shared among several functions and
by all threads of the process.  The second requires the user to handle
the state.

   All functions have in common that they use the same congruential
formula with the same constants.  The formula is

     Y = (a * X + c) mod m

where X is the state of the generator at the beginning and Y the state
at the end.  `a' and `c' are constants determining the way the
generator works.  By default they are

     a = 0x5DEECE66D = 25214903917
     c = 0xb = 11

but they can also be changed by the user.  `m' is of course 2^48 since
the state consists of a 48-bit array.

   The prototypes for these functions are in `stdlib.h'.  

 -- Function: double drand48 (void)
     This function returns a `double' value in the range of `0.0' to
     `1.0' (exclusive).  The random bits are determined by the global
     state of the random number generator in the C library.

     Since the `double' type according to IEEE 754 has a 52-bit
     mantissa this means 4 bits are not initialized by the random number
     generator.  These are (of course) chosen to be the least
     significant bits and they are initialized to `0'.

 -- Function: double erand48 (unsigned short int XSUBI[3])
     This function returns a `double' value in the range of `0.0' to
     `1.0' (exclusive), similarly to `drand48'.  The argument is an
     array describing the state of the random number generator.

     This function can be called subsequently since it updates the
     array to guarantee random numbers.  The array should have been
     initialized before initial use to obtain reproducible results.

 -- Function: long int lrand48 (void)
     The `lrand48' function returns an integer value in the range of
     `0' to `2^31' (exclusive).  Even if the size of the `long int'
     type can take more than 32 bits, no higher numbers are returned.
     The random bits are determined by the global state of the random
     number generator in the C library.

 -- Function: long int nrand48 (unsigned short int XSUBI[3])
     This function is similar to the `lrand48' function in that it
     returns a number in the range of `0' to `2^31' (exclusive) but the
     state of the random number generator used to produce the random
     bits is determined by the array provided as the parameter to the
     function.

     The numbers in the array are updated afterwards so that subsequent
     calls to this function yield different results (as is expected of
     a random number generator).  The array should have been
     initialized before the first call to obtain reproducible results.

 -- Function: long int mrand48 (void)
     The `mrand48' function is similar to `lrand48'.  The only
     difference is that the numbers returned are in the range `-2^31' to
     `2^31' (exclusive).

 -- Function: long int jrand48 (unsigned short int XSUBI[3])
     The `jrand48' function is similar to `nrand48'.  The only
     difference is that the numbers returned are in the range `-2^31' to
     `2^31' (exclusive).  For the `xsubi' parameter the same
     requirements are necessary.

   The internal state of the random number generator can be initialized
in several ways.  The methods differ in the completeness of the
information provided.

 -- Function: void srand48 (long int SEEDVAL)
     The `srand48' function sets the most significant 32 bits of the
     internal state of the random number generator to the least
     significant 32 bits of the SEEDVAL parameter.  The lower 16 bits
     are initialized to the value `0x330E'.  Even if the `long int'
     type contains more than 32 bits only the lower 32 bits are used.

     Owing to this limitation, initialization of the state of this
     function is not very useful.  But it makes it easy to use a
     construct like `srand48 (time (0))'.

     A side-effect of this function is that the values `a' and `c' from
     the internal state, which are used in the congruential formula,
     are reset to the default values given above.  This is of
     importance once the user has called the `lcong48' function (see
     below).

 -- Function: unsigned short int * seed48 (unsigned short int
          SEED16V[3])
     The `seed48' function initializes all 48 bits of the state of the
     internal random number generator from the contents of the parameter
     SEED16V.  Here the lower 16 bits of the first element of SEE16V
     initialize the least significant 16 bits of the internal state,
     the lower 16 bits of `SEED16V[1]' initialize the mid-order 16 bits
     of the state and the 16 lower bits of `SEED16V[2]' initialize the
     most significant 16 bits of the state.

     Unlike `srand48' this function lets the user initialize all 48 bits
     of the state.

     The value returned by `seed48' is a pointer to an array containing
     the values of the internal state before the change.  This might be
     useful to restart the random number generator at a certain state.
     Otherwise the value can simply be ignored.

     As for `srand48', the values `a' and `c' from the congruential
     formula are reset to the default values.

   There is one more function to initialize the random number generator
which enables you to specify even more information by allowing you to
change the parameters in the congruential formula.

 -- Function: void lcong48 (unsigned short int PARAM[7])
     The `lcong48' function allows the user to change the complete state
     of the random number generator.  Unlike `srand48' and `seed48',
     this function also changes the constants in the congruential
     formula.

     From the seven elements in the array PARAM the least significant
     16 bits of the entries `PARAM[0]' to `PARAM[2]' determine the
     initial state, the least significant 16 bits of `PARAM[3]' to
     `PARAM[5]' determine the 48 bit constant `a' and `PARAM[6]'
     determines the 16-bit value `c'.

   All the above functions have in common that they use the global
parameters for the congruential formula.  In multi-threaded programs it
might sometimes be useful to have different parameters in different
threads.  For this reason all the above functions have a counterpart
which works on a description of the random number generator in the
user-supplied buffer instead of the global state.

   Please note that it is no problem if several threads use the global
state if all threads use the functions which take a pointer to an array
containing the state.  The random numbers are computed following the
same loop but if the state in the array is different all threads will
obtain an individual random number generator.

   The user-supplied buffer must be of type `struct drand48_data'.
This type should be regarded as opaque and not manipulated directly.

 -- Function: int drand48_r (struct drand48_data *BUFFER, double
          *RESULT)
     This function is equivalent to the `drand48' function with the
     difference that it does not modify the global random number
     generator parameters but instead the parameters in the buffer
     supplied through the pointer BUFFER.  The random number is
     returned in the variable pointed to by RESULT.

     The return value of the function indicates whether the call
     succeeded.  If the value is less than `0' an error occurred and
     ERRNO is set to indicate the problem.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int erand48_r (unsigned short int XSUBI[3], struct
          drand48_data *BUFFER, double *RESULT)
     The `erand48_r' function works like `erand48', but in addition it
     takes an argument BUFFER which describes the random number
     generator.  The state of the random number generator is taken from
     the `xsubi' array, the parameters for the congruential formula
     from the global random number generator data.  The random number
     is returned in the variable pointed to by RESULT.

     The return value is non-negative if the call succeeded.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int lrand48_r (struct drand48_data *BUFFER, double
          *RESULT)
     This function is similar to `lrand48', but in addition it takes a
     pointer to a buffer describing the state of the random number
     generator just like `drand48'.

     If the return value of the function is non-negative the variable
     pointed to by RESULT contains the result.  Otherwise an error
     occurred.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int nrand48_r (unsigned short int XSUBI[3], struct
          drand48_data *BUFFER, long int *RESULT)
     The `nrand48_r' function works like `nrand48' in that it produces
     a random number in the range `0' to `2^31'.  But instead of using
     the global parameters for the congruential formula it uses the
     information from the buffer pointed to by BUFFER.  The state is
     described by the values in XSUBI.

     If the return value is non-negative the variable pointed to by
     RESULT contains the result.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int mrand48_r (struct drand48_data *BUFFER, double
          *RESULT)
     This function is similar to `mrand48' but like the other reentrant
     functions it uses the random number generator described by the
     value in the buffer pointed to by BUFFER.

     If the return value is non-negative the variable pointed to by
     RESULT contains the result.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int jrand48_r (unsigned short int XSUBI[3], struct
          drand48_data *BUFFER, long int *RESULT)
     The `jrand48_r' function is similar to `jrand48'.  Like the other
     reentrant functions of this function family it uses the
     congruential formula parameters from the buffer pointed to by
     BUFFER.

     If the return value is non-negative the variable pointed to by
     RESULT contains the result.

     This function is a GNU extension and should not be used in portable
     programs.

   Before any of the above functions are used the buffer of type
`struct drand48_data' should be initialized.  The easiest way to do
this is to fill the whole buffer with null bytes, e.g. by

     memset (buffer, '\0', sizeof (struct drand48_data));

Using any of the reentrant functions of this family now will
automatically initialize the random number generator to the default
values for the state and the parameters of the congruential formula.

   The other possibility is to use any of the functions which explicitly
initialize the buffer.  Though it might be obvious how to initialize the
buffer from looking at the parameter to the function, it is highly
recommended to use these functions since the result might not always be
what you expect.

 -- Function: int srand48_r (long int SEEDVAL, struct drand48_data
          *BUFFER)
     The description of the random number generator represented by the
     information in BUFFER is initialized similarly to what the function
     `srand48' does.  The state is initialized from the parameter
     SEEDVAL and the parameters for the congruential formula are
     initialized to their default values.

     If the return value is non-negative the function call succeeded.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int seed48_r (unsigned short int SEED16V[3], struct
          drand48_data *BUFFER)
     This function is similar to `srand48_r' but like `seed48' it
     initializes all 48 bits of the state from the parameter SEED16V.

     If the return value is non-negative the function call succeeded.
     It does not return a pointer to the previous state of the random
     number generator like the `seed48' function does.  If the user
     wants to preserve the state for a later re-run s/he can copy the
     whole buffer pointed to by BUFFER.

     This function is a GNU extension and should not be used in portable
     programs.

 -- Function: int lcong48_r (unsigned short int PARAM[7], struct
          drand48_data *BUFFER)
     This function initializes all aspects of the random number
     generator described in BUFFER with the data in PARAM.  Here it is
     especially true that the function does more than just copying the
     contents of PARAM and BUFFER.  More work is required and therefore
     it is important to use this function rather than initializing the
     random number generator directly.

     If the return value is non-negative the function call succeeded.

     This function is a GNU extension and should not be used in portable
     programs.


File: libc.info,  Node: FP Function Optimizations,  Prev: Pseudo-Random Numbers,  Up: Mathematics

19.9 Is Fast Code or Small Code preferred?
==========================================

If an application uses many floating point functions it is often the
case that the cost of the function calls themselves is not negligible.
Modern processors can often execute the operations themselves very
fast, but the function call disrupts the instruction pipeline.

   For this reason the GNU C Library provides optimizations for many of
the frequently-used math functions.  When GNU CC is used and the user
activates the optimizer, several new inline functions and macros are
defined.  These new functions and macros have the same names as the
library functions and so are used instead of the latter.  In the case of
inline functions the compiler will decide whether it is reasonable to
use them, and this decision is usually correct.

   This means that no calls to the library functions may be necessary,
and can increase the speed of generated code significantly.  The
drawback is that code size will increase, and the increase is not
always negligible.

   There are two kind of inline functions: Those that give the same
result as the library functions and others that might not set `errno'
and might have a reduced precision and/or argument range in comparison
with the library functions.  The latter inline functions are only
available if the flag `-ffast-math' is given to GNU CC.

   In cases where the inline functions and macros are not wanted the
symbol `__NO_MATH_INLINES' should be defined before any system header is
included.  This will ensure that only library functions are used.  Of
course, it can be determined for each file in the project whether
giving this option is preferable or not.

   Not all hardware implements the entire IEEE 754 standard, and even
if it does there may be a substantial performance penalty for using some
of its features.  For example, enabling traps on some processors forces
the FPU to run un-pipelined, which can more than double calculation
time.


File: libc.info,  Node: Arithmetic,  Next: Date and Time,  Prev: Mathematics,  Up: Top

20 Arithmetic Functions
***********************

This chapter contains information about functions for doing basic
arithmetic operations, such as splitting a float into its integer and
fractional parts or retrieving the imaginary part of a complex value.
These functions are declared in the header files `math.h' and
`complex.h'.

* Menu:

* Integers::                    Basic integer types and concepts
* Integer Division::            Integer division with guaranteed rounding.
* Floating Point Numbers::      Basic concepts.  IEEE 754.
* Floating Point Classes::      The five kinds of floating-point number.
* Floating Point Errors::       When something goes wrong in a calculation.
* Rounding::                    Controlling how results are rounded.
* Control Functions::           Saving and restoring the FPU's state.
* Arithmetic Functions::        Fundamental operations provided by the library.
* Complex Numbers::             The types.  Writing complex constants.
* Operations on Complex::       Projection, conjugation, decomposition.
* Parsing of Numbers::          Converting strings to numbers.
* System V Number Conversion::  An archaic way to convert numbers to strings.


File: libc.info,  Node: Integers,  Next: Integer Division,  Up: Arithmetic

20.1 Integers
=============

The C language defines several integer data types: integer, short
integer, long integer, and character, all in both signed and unsigned
varieties.  The GNU C compiler extends the language to contain long
long integers as well.  

   The C integer types were intended to allow code to be portable among
machines with different inherent data sizes (word sizes), so each type
may have different ranges on different machines.  The problem with this
is that a program often needs to be written for a particular range of
integers, and sometimes must be written for a particular size of
storage, regardless of what machine the program runs on.

   To address this problem, the GNU C library contains C type
definitions you can use to declare integers that meet your exact needs.
Because the GNU C library header files are customized to a specific
machine, your program source code doesn't have to be.

   These `typedef's are in `stdint.h'.  

   If you require that an integer be represented in exactly N bits, use
one of the following types, with the obvious mapping to bit size and
signedness:

   * int8_t

   * int16_t

   * int32_t

   * int64_t

   * uint8_t

   * uint16_t

   * uint32_t

   * uint64_t

   If your C compiler and target machine do not allow integers of a
certain size, the corresponding above type does not exist.

   If you don't need a specific storage size, but want the smallest data
structure with _at least_ N bits, use one of these:

   * int_least8_t

   * int_least16_t

   * int_least32_t

   * int_least64_t

   * uint_least8_t

   * uint_least16_t

   * uint_least32_t

   * uint_least64_t

   If you don't need a specific storage size, but want the data
structure that allows the fastest access while having at least N bits
(and among data structures with the same access speed, the smallest
one), use one of these:

   * int_fast8_t

   * int_fast16_t

   * int_fast32_t

   * int_fast64_t

   * uint_fast8_t

   * uint_fast16_t

   * uint_fast32_t

   * uint_fast64_t

   If you want an integer with the widest range possible on the
platform on which it is being used, use one of the following.  If you
use these, you should write code that takes into account the variable
size and range of the integer.

   * intmax_t

   * uintmax_t

   The GNU C library also provides macros that tell you the maximum and
minimum possible values for each integer data type.  The macro names
follow these examples: `INT32_MAX', `UINT8_MAX', `INT_FAST32_MIN',
`INT_LEAST64_MIN', `UINTMAX_MAX', `INTMAX_MAX', `INTMAX_MIN'.  Note
that there are no macros for unsigned integer minima.  These are always
zero.  

   There are similar macros for use with C's built in integer types
which should come with your C compiler.  These are described in *Note
Data Type Measurements::.

   Don't forget you can use the C `sizeof' function with any of these
data types to get the number of bytes of storage each uses.


File: libc.info,  Node: Integer Division,  Next: Floating Point Numbers,  Prev: Integers,  Up: Arithmetic

20.2 Integer Division
=====================

This section describes functions for performing integer division.  These
functions are redundant when GNU CC is used, because in GNU C the `/'
operator always rounds towards zero.  But in other C implementations,
`/' may round differently with negative arguments.  `div' and `ldiv'
are useful because they specify how to round the quotient: towards
zero.  The remainder has the same sign as the numerator.

   These functions are specified to return a result R such that the
value `R.quot*DENOMINATOR + R.rem' equals NUMERATOR.

   To use these facilities, you should include the header file
`stdlib.h' in your program.

 -- Data Type: div_t
     This is a structure type used to hold the result returned by the
     `div' function.  It has the following members:

    `int quot'
          The quotient from the division.

    `int rem'
          The remainder from the division.

 -- Function: div_t div (int NUMERATOR, int DENOMINATOR)
     This function `div' computes the quotient and remainder from the
     division of NUMERATOR by DENOMINATOR, returning the result in a
     structure of type `div_t'.

     If the result cannot be represented (as in a division by zero), the
     behavior is undefined.

     Here is an example, albeit not a very useful one.

          div_t result;
          result = div (20, -6);

     Now `result.quot' is `-3' and `result.rem' is `2'.

 -- Data Type: ldiv_t
     This is a structure type used to hold the result returned by the
     `ldiv' function.  It has the following members:

    `long int quot'
          The quotient from the division.

    `long int rem'
          The remainder from the division.

     (This is identical to `div_t' except that the components are of
     type `long int' rather than `int'.)

 -- Function: ldiv_t ldiv (long int NUMERATOR, long int DENOMINATOR)
     The `ldiv' function is similar to `div', except that the arguments
     are of type `long int' and the result is returned as a structure
     of type `ldiv_t'.

 -- Data Type: lldiv_t
     This is a structure type used to hold the result returned by the
     `lldiv' function.  It has the following members:

    `long long int quot'
          The quotient from the division.

    `long long int rem'
          The remainder from the division.

     (This is identical to `div_t' except that the components are of
     type `long long int' rather than `int'.)

 -- Function: lldiv_t lldiv (long long int NUMERATOR, long long int
          DENOMINATOR)
     The `lldiv' function is like the `div' function, but the arguments
     are of type `long long int' and the result is returned as a
     structure of type `lldiv_t'.

     The `lldiv' function was added in ISO C99.

 -- Data Type: imaxdiv_t
     This is a structure type used to hold the result returned by the
     `imaxdiv' function.  It has the following members:

    `intmax_t quot'
          The quotient from the division.

    `intmax_t rem'
          The remainder from the division.

     (This is identical to `div_t' except that the components are of
     type `intmax_t' rather than `int'.)

     See *Note Integers:: for a description of the `intmax_t' type.


 -- Function: imaxdiv_t imaxdiv (intmax_t NUMERATOR, intmax_t
          DENOMINATOR)
     The `imaxdiv' function is like the `div' function, but the
     arguments are of type `intmax_t' and the result is returned as a
     structure of type `imaxdiv_t'.

     See *Note Integers:: for a description of the `intmax_t' type.

     The `imaxdiv' function was added in ISO C99.


File: libc.info,  Node: Floating Point Numbers,  Next: Floating Point Classes,  Prev: Integer Division,  Up: Arithmetic

20.3 Floating Point Numbers
===========================

Most computer hardware has support for two different kinds of numbers:
integers (...-3, -2, -1, 0, 1, 2, 3...) and floating-point numbers.
Floating-point numbers have three parts: the "mantissa", the
"exponent", and the "sign bit".  The real number represented by a
floating-point value is given by (s ? -1 : 1) * 2^e * M where s is the
sign bit, e the exponent, and M the mantissa.  *Note Floating Point
Concepts::, for details.  (It is possible to have a different "base"
for the exponent, but all modern hardware uses 2.)

   Floating-point numbers can represent a finite subset of the real
numbers.  While this subset is large enough for most purposes, it is
important to remember that the only reals that can be represented
exactly are rational numbers that have a terminating binary expansion
shorter than the width of the mantissa.  Even simple fractions such as
1/5 can only be approximated by floating point.

   Mathematical operations and functions frequently need to produce
values that are not representable.  Often these values can be
approximated closely enough for practical purposes, but sometimes they
can't.  Historically there was no way to tell when the results of a
calculation were inaccurate.  Modern computers implement the IEEE 754
standard for numerical computations, which defines a framework for
indicating to the program when the results of calculation are not
trustworthy.  This framework consists of a set of "exceptions" that
indicate why a result could not be represented, and the special values
"infinity" and "not a number" (NaN).


File: libc.info,  Node: Floating Point Classes,  Next: Floating Point Errors,  Prev: Floating Point Numbers,  Up: Arithmetic

20.4 Floating-Point Number Classification Functions
===================================================

ISO C99 defines macros that let you determine what sort of
floating-point number a variable holds.

 -- Macro: int fpclassify (_float-type_ X)
     This is a generic macro which works on all floating-point types and
     which returns a value of type `int'.  The possible values are:

    `FP_NAN'
          The floating-point number X is "Not a Number" (*note Infinity
          and NaN::)

    `FP_INFINITE'
          The value of X is either plus or minus infinity (*note
          Infinity and NaN::)

    `FP_ZERO'
          The value of X is zero.  In floating-point formats like
          IEEE 754, where zero can be signed, this value is also
          returned if X is negative zero.

    `FP_SUBNORMAL'
          Numbers whose absolute value is too small to be represented
          in the normal format are represented in an alternate,
          "denormalized" format (*note Floating Point Concepts::).
          This format is less precise but can represent values closer
          to zero.  `fpclassify' returns this value for values of X in
          this alternate format.

    `FP_NORMAL'
          This value is returned for all other values of X.  It
          indicates that there is nothing special about the number.


   `fpclassify' is most useful if more than one property of a number
must be tested.  There are more specific macros which only test one
property at a time.  Generally these macros execute faster than
`fpclassify', since there is special hardware support for them.  You
should therefore use the specific macros whenever possible.

 -- Macro: int isfinite (_float-type_ X)
     This macro returns a nonzero value if X is finite: not plus or
     minus infinity, and not NaN.  It is equivalent to

          (fpclassify (x) != FP_NAN && fpclassify (x) != FP_INFINITE)

     `isfinite' is implemented as a macro which accepts any
     floating-point type.

 -- Macro: int isnormal (_float-type_ X)
     This macro returns a nonzero value if X is finite and normalized.
     It is equivalent to

          (fpclassify (x) == FP_NORMAL)

 -- Macro: int isnan (_float-type_ X)
     This macro returns a nonzero value if X is NaN.  It is equivalent
     to

          (fpclassify (x) == FP_NAN)

   Another set of floating-point classification functions was provided
by BSD.  The GNU C library also supports these functions; however, we
recommend that you use the ISO C99 macros in new code.  Those are
standard and will be available more widely.  Also, since they are
macros, you do not have to worry about the type of their argument.

 -- Function: int isinf (double X)
 -- Function: int isinff (float X)
 -- Function: int isinfl (long double X)
     This function returns `-1' if X represents negative infinity, `1'
     if X represents positive infinity, and `0' otherwise.

 -- Function: int isnan (double X)
 -- Function: int isnanf (float X)
 -- Function: int isnanl (long double X)
     This function returns a nonzero value if X is a "not a number"
     value, and zero otherwise.

     *Note_* The `isnan' macro defined by ISO C99 overrides the BSD
     function.  This is normally not a problem, because the two
     routines behave identically.  However, if you really need to get
     the BSD function for some reason, you can write

          (isnan) (x)

 -- Function: int finite (double X)
 -- Function: int finitef (float X)
 -- Function: int finitel (long double X)
     This function returns a nonzero value if X is finite or a "not a
     number" value, and zero otherwise.

   *Portability Note:* The functions listed in this section are BSD
extensions.


File: libc.info,  Node: Floating Point Errors,  Next: Rounding,  Prev: Floating Point Classes,  Up: Arithmetic

20.5 Errors in Floating-Point Calculations
==========================================

* Menu:

* FP Exceptions::               IEEE 754 math exceptions and how to detect them.
* Infinity and NaN::            Special values returned by calculations.
* Status bit operations::       Checking for exceptions after the fact.
* Math Error Reporting::        How the math functions report errors.


File: libc.info,  Node: FP Exceptions,  Next: Infinity and NaN,  Up: Floating Point Errors

20.5.1 FP Exceptions
--------------------

The IEEE 754 standard defines five "exceptions" that can occur during a
calculation.  Each corresponds to a particular sort of error, such as
overflow.

   When exceptions occur (when exceptions are "raised", in the language
of the standard), one of two things can happen.  By default the
exception is simply noted in the floating-point "status word", and the
program continues as if nothing had happened.  The operation produces a
default value, which depends on the exception (see the table below).
Your program can check the status word to find out which exceptions
happened.

   Alternatively, you can enable "traps" for exceptions.  In that case,
when an exception is raised, your program will receive the `SIGFPE'
signal.  The default action for this signal is to terminate the
program.  *Note Signal Handling::, for how you can change the effect of
the signal.

   In the System V math library, the user-defined function `matherr' is
called when certain exceptions occur inside math library functions.
However, the Unix98 standard deprecates this interface.  We support it
for historical compatibility, but recommend that you do not use it in
new programs.

The exceptions defined in IEEE 754 are:

`Invalid Operation'
     This exception is raised if the given operands are invalid for the
     operation to be performed.  Examples are (see IEEE 754, section 7):
       1. Addition or subtraction: oo - oo.  (But oo + oo = oo).

       2. Multiplication: 0 * oo.

       3. Division: 0/0 or oo/oo.

       4. Remainder: x REM y, where y is zero or x is infinite.

       5. Square root if the operand is less then zero.  More
          generally, any mathematical function evaluated outside its
          domain produces this exception.

       6. Conversion of a floating-point number to an integer or decimal
          string, when the number cannot be represented in the target
          format (due to overflow, infinity, or NaN).

       7. Conversion of an unrecognizable input string.

       8. Comparison via predicates involving < or >, when one or other
          of the operands is NaN.  You can prevent this exception by
          using the unordered comparison functions instead; see *Note
          FP Comparison Functions::.

     If the exception does not trap, the result of the operation is NaN.

`Division by Zero'
     This exception is raised when a finite nonzero number is divided
     by zero.  If no trap occurs the result is either +oo or -oo,
     depending on the signs of the operands.

`Overflow'
     This exception is raised whenever the result cannot be represented
     as a finite value in the precision format of the destination.  If
     no trap occurs the result depends on the sign of the intermediate
     result and the current rounding mode (IEEE 754, section 7.3):
       1. Round to nearest carries all overflows to oo with the sign of
          the intermediate result.

       2. Round toward 0 carries all overflows to the largest
          representable finite number with the sign of the intermediate
          result.

       3. Round toward -oo carries positive overflows to the largest
          representable finite number and negative overflows to -oo.

       4. Round toward oo carries negative overflows to the most
          negative representable finite number and positive overflows
          to oo.

     Whenever the overflow exception is raised, the inexact exception
     is also raised.

`Underflow'
     The underflow exception is raised when an intermediate result is
     too small to be calculated accurately, or if the operation's
     result rounded to the destination precision is too small to be
     normalized.

     When no trap is installed for the underflow exception, underflow is
     signaled (via the underflow flag) only when both tininess and loss
     of accuracy have been detected.  If no trap handler is installed
     the operation continues with an imprecise small value, or zero if
     the destination precision cannot hold the small exact result.

`Inexact'
     This exception is signalled if a rounded result is not exact (such
     as when calculating the square root of two) or a result overflows
     without an overflow trap.


File: libc.info,  Node: Infinity and NaN,  Next: Status bit operations,  Prev: FP Exceptions,  Up: Floating Point Errors

20.5.2 Infinity and NaN
-----------------------

IEEE 754 floating point numbers can represent positive or negative
infinity, and "NaN" (not a number).  These three values arise from
calculations whose result is undefined or cannot be represented
accurately.  You can also deliberately set a floating-point variable to
any of them, which is sometimes useful.  Some examples of calculations
that produce infinity or NaN:

     1/0 = oo
     log (0) = -oo
     sqrt (-1) = NaN

   When a calculation produces any of these values, an exception also
occurs; see *Note FP Exceptions::.

   The basic operations and math functions all accept infinity and NaN
and produce sensible output.  Infinities propagate through calculations
as one would expect: for example, 2 + oo = oo, 4/oo = 0, atan (oo) =
pi/2.  NaN, on the other hand, infects any calculation that involves
it.  Unless the calculation would produce the same result no matter
what real value replaced NaN, the result is NaN.

   In comparison operations, positive infinity is larger than all values
except itself and NaN, and negative infinity is smaller than all values
except itself and NaN.  NaN is "unordered": it is not equal to, greater
than, or less than anything, _including itself_. `x == x' is false if
the value of `x' is NaN.  You can use this to test whether a value is
NaN or not, but the recommended way to test for NaN is with the `isnan'
function (*note Floating Point Classes::).  In addition, `<', `>',
`<=', and `>=' will raise an exception when applied to NaNs.

   `math.h' defines macros that allow you to explicitly set a variable
to infinity or NaN.

 -- Macro: float INFINITY
     An expression representing positive infinity.  It is equal to the
     value produced  by mathematical operations like `1.0 / 0.0'.
     `-INFINITY' represents negative infinity.

     You can test whether a floating-point value is infinite by
     comparing it to this macro.  However, this is not recommended; you
     should use the `isfinite' macro instead.  *Note Floating Point
     Classes::.

     This macro was introduced in the ISO C99 standard.

 -- Macro: float NAN
     An expression representing a value which is "not a number".  This
     macro is a GNU extension, available only on machines that support
     the "not a number" value--that is to say, on all machines that
     support IEEE floating point.

     You can use `#ifdef NAN' to test whether the machine supports NaN.
     (Of course, you must arrange for GNU extensions to be visible,
     such as by defining `_GNU_SOURCE', and then you must include
     `math.h'.)

   IEEE 754 also allows for another unusual value: negative zero.  This
value is produced when you divide a positive number by negative
infinity, or when a negative result is smaller than the limits of
representation.  Negative zero behaves identically to zero in all
calculations, unless you explicitly test the sign bit with `signbit' or
`copysign'.


File: libc.info,  Node: Status bit operations,  Next: Math Error Reporting,  Prev: Infinity and NaN,  Up: Floating Point Errors

20.5.3 Examining the FPU status word
------------------------------------

ISO C99 defines functions to query and manipulate the floating-point
status word.  You can use these functions to check for untrapped
exceptions when it's convenient, rather than worrying about them in the
middle of a calculation.

   These constants represent the various IEEE 754 exceptions.  Not all
FPUs report all the different exceptions.  Each constant is defined if
and only if the FPU you are compiling for supports that exception, so
you can test for FPU support with `#ifdef'.  They are defined in
`fenv.h'.

`FE_INEXACT'
     The inexact exception.

`FE_DIVBYZERO'
     The divide by zero exception.

`FE_UNDERFLOW'
     The underflow exception.

`FE_OVERFLOW'
     The overflow exception.

`FE_INVALID'
     The invalid exception.

   The macro `FE_ALL_EXCEPT' is the bitwise OR of all exception macros
which are supported by the FP implementation.

   These functions allow you to clear exception flags, test for
exceptions, and save and restore the set of exceptions flagged.

 -- Function: int feclearexcept (int EXCEPTS)
     This function clears all of the supported exception flags
     indicated by EXCEPTS.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

 -- Function: int feraiseexcept (int EXCEPTS)
     This function raises the supported exceptions indicated by
     EXCEPTS.  If more than one exception bit in EXCEPTS is set the
     order in which the exceptions are raised is undefined except that
     overflow (`FE_OVERFLOW') or underflow (`FE_UNDERFLOW') are raised
     before inexact (`FE_INEXACT').  Whether for overflow or underflow
     the inexact exception is also raised is also implementation
     dependent.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

 -- Function: int fetestexcept (int EXCEPTS)
     Test whether the exception flags indicated by the parameter EXCEPT
     are currently set.  If any of them are, a nonzero value is returned
     which specifies which exceptions are set.  Otherwise the result is
     zero.

   To understand these functions, imagine that the status word is an
integer variable named STATUS.  `feclearexcept' is then equivalent to
`status &= ~excepts' and `fetestexcept' is equivalent to `(status &
excepts)'.  The actual implementation may be very different, of course.

   Exception flags are only cleared when the program explicitly
requests it, by calling `feclearexcept'.  If you want to check for
exceptions from a set of calculations, you should clear all the flags
first.  Here is a simple example of the way to use `fetestexcept':

     {
       double f;
       int raised;
       feclearexcept (FE_ALL_EXCEPT);
       f = compute ();
       raised = fetestexcept (FE_OVERFLOW | FE_INVALID);
       if (raised & FE_OVERFLOW) { /* ... */ }
       if (raised & FE_INVALID) { /* ... */ }
       /* ... */
     }

   You cannot explicitly set bits in the status word.  You can, however,
save the entire status word and restore it later.  This is done with the
following functions:

 -- Function: int fegetexceptflag (fexcept_t *FLAGP, int EXCEPTS)
     This function stores in the variable pointed to by FLAGP an
     implementation-defined value representing the current setting of
     the exception flags indicated by EXCEPTS.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

 -- Function: int fesetexceptflag (const fexcept_t *FLAGP, int
     EXCEPTS) This function restores the flags for the exceptions
     indicated by EXCEPTS to the values stored in the variable pointed
     to by FLAGP.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

   Note that the value stored in `fexcept_t' bears no resemblance to
the bit mask returned by `fetestexcept'.  The type may not even be an
integer.  Do not attempt to modify an `fexcept_t' variable.


File: libc.info,  Node: Math Error Reporting,  Prev: Status bit operations,  Up: Floating Point Errors

20.5.4 Error Reporting by Mathematical Functions
------------------------------------------------

Many of the math functions are defined only over a subset of the real or
complex numbers.  Even if they are mathematically defined, their result
may be larger or smaller than the range representable by their return
type.  These are known as "domain errors", "overflows", and
"underflows", respectively.  Math functions do several things when one
of these errors occurs.  In this manual we will refer to the complete
response as "signalling" a domain error, overflow, or underflow.

   When a math function suffers a domain error, it raises the invalid
exception and returns NaN.  It also sets ERRNO to `EDOM'; this is for
compatibility with old systems that do not support IEEE 754 exception
handling.  Likewise, when overflow occurs, math functions raise the
overflow exception and return oo or -oo as appropriate.  They also set
ERRNO to `ERANGE'.  When underflow occurs, the underflow exception is
raised, and zero (appropriately signed) is returned.  ERRNO may be set
to `ERANGE', but this is not guaranteed.

   Some of the math functions are defined mathematically to result in a
complex value over parts of their domains.  The most familiar example of
this is taking the square root of a negative number.  The complex math
functions, such as `csqrt', will return the appropriate complex value
in this case.  The real-valued functions, such as `sqrt', will signal a
domain error.

   Some older hardware does not support infinities.  On that hardware,
overflows instead return a particular very large number (usually the
largest representable number).  `math.h' defines macros you can use to
test for overflow on both old and new hardware.

 -- Macro: double HUGE_VAL
 -- Macro: float HUGE_VALF
 -- Macro: long double HUGE_VALL
     An expression representing a particular very large number.  On
     machines that use IEEE 754 floating point format, `HUGE_VAL' is
     infinity.  On other machines, it's typically the largest positive
     number that can be represented.

     Mathematical functions return the appropriately typed version of
     `HUGE_VAL' or `-HUGE_VAL' when the result is too large to be
     represented.


File: libc.info,  Node: Rounding,  Next: Control Functions,  Prev: Floating Point Errors,  Up: Arithmetic

20.6 Rounding Modes
===================

Floating-point calculations are carried out internally with extra
precision, and then rounded to fit into the destination type.  This
ensures that results are as precise as the input data.  IEEE 754
defines four possible rounding modes:

Round to nearest.
     This is the default mode.  It should be used unless there is a
     specific need for one of the others.  In this mode results are
     rounded to the nearest representable value.  If the result is
     midway between two representable values, the even representable is
     chosen. "Even" here means the lowest-order bit is zero.  This
     rounding mode prevents statistical bias and guarantees numeric
     stability: round-off errors in a lengthy calculation will remain
     smaller than half of `FLT_EPSILON'.

Round toward plus Infinity.
     All results are rounded to the smallest representable value which
     is greater than the result.

Round toward minus Infinity.
     All results are rounded to the largest representable value which
     is less than the result.

Round toward zero.
     All results are rounded to the largest representable value whose
     magnitude is less than that of the result.  In other words, if the
     result is negative it is rounded up; if it is positive, it is
     rounded down.

`fenv.h' defines constants which you can use to refer to the various
rounding modes.  Each one will be defined if and only if the FPU
supports the corresponding rounding mode.

`FE_TONEAREST'
     Round to nearest.

`FE_UPWARD'
     Round toward +oo.

`FE_DOWNWARD'
     Round toward -oo.

`FE_TOWARDZERO'
     Round toward zero.

   Underflow is an unusual case.  Normally, IEEE 754 floating point
numbers are always normalized (*note Floating Point Concepts::).
Numbers smaller than 2^r (where r is the minimum exponent,
`FLT_MIN_RADIX-1' for FLOAT) cannot be represented as normalized
numbers.  Rounding all such numbers to zero or 2^r would cause some
algorithms to fail at 0.  Therefore, they are left in denormalized
form.  That produces loss of precision, since some bits of the mantissa
are stolen to indicate the decimal point.

   If a result is too small to be represented as a denormalized number,
it is rounded to zero.  However, the sign of the result is preserved; if
the calculation was negative, the result is "negative zero".  Negative
zero can also result from some operations on infinity, such as 4/-oo.
Negative zero behaves identically to zero except when the `copysign' or
`signbit' functions are used to check the sign bit directly.

   At any time one of the above four rounding modes is selected.  You
can find out which one with this function:

 -- Function: int fegetround (void)
     Returns the currently selected rounding mode, represented by one
     of the values of the defined rounding mode macros.

To change the rounding mode, use this function:

 -- Function: int fesetround (int ROUND)
     Changes the currently selected rounding mode to ROUND.  If ROUND
     does not correspond to one of the supported rounding modes nothing
     is changed.  `fesetround' returns zero if it changed the rounding
     mode, a nonzero value if the mode is not supported.

   You should avoid changing the rounding mode if possible.  It can be
an expensive operation; also, some hardware requires you to compile your
program differently for it to work.  The resulting code may run slower.
See your compiler documentation for details.


File: libc.info,  Node: Control Functions,  Next: Arithmetic Functions,  Prev: Rounding,  Up: Arithmetic

20.7 Floating-Point Control Functions
=====================================

IEEE 754 floating-point implementations allow the programmer to decide
whether traps will occur for each of the exceptions, by setting bits in
the "control word".  In C, traps result in the program receiving the
`SIGFPE' signal; see *Note Signal Handling::.

   *Note_* IEEE 754 says that trap handlers are given details of the
exceptional situation, and can set the result value.  C signals do not
provide any mechanism to pass this information back and forth.
Trapping exceptions in C is therefore not very useful.

   It is sometimes necessary to save the state of the floating-point
unit while you perform some calculation.  The library provides functions
which save and restore the exception flags, the set of exceptions that
generate traps, and the rounding mode.  This information is known as the
"floating-point environment".

   The functions to save and restore the floating-point environment all
use a variable of type `fenv_t' to store information.  This type is
defined in `fenv.h'.  Its size and contents are implementation-defined.
You should not attempt to manipulate a variable of this type directly.

   To save the state of the FPU, use one of these functions:

 -- Function: int fegetenv (fenv_t *ENVP)
     Store the floating-point environment in the variable pointed to by
     ENVP.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

 -- Function: int feholdexcept (fenv_t *ENVP)
     Store the current floating-point environment in the object pointed
     to by ENVP.  Then clear all exception flags, and set the FPU to
     trap no exceptions.  Not all FPUs support trapping no exceptions;
     if `feholdexcept' cannot set this mode, it returns nonzero value.
     If it succeeds, it returns zero.

   The functions which restore the floating-point environment can take
these kinds of arguments:

   * Pointers to `fenv_t' objects, which were initialized previously by
     a call to `fegetenv' or `feholdexcept'.

   * The special macro `FE_DFL_ENV' which represents the floating-point
     environment as it was available at program start.

   * Implementation defined macros with names starting with `FE_' and
     having type `fenv_t *'.

     If possible, the GNU C Library defines a macro `FE_NOMASK_ENV'
     which represents an environment where every exception raised
     causes a trap to occur.  You can test for this macro using
     `#ifdef'.  It is only defined if `_GNU_SOURCE' is defined.

     Some platforms might define other predefined environments.

To set the floating-point environment, you can use either of these
functions:

 -- Function: int fesetenv (const fenv_t *ENVP)
     Set the floating-point environment to that described by ENVP.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

 -- Function: int feupdateenv (const fenv_t *ENVP)
     Like `fesetenv', this function sets the floating-point environment
     to that described by ENVP.  However, if any exceptions were
     flagged in the status word before `feupdateenv' was called, they
     remain flagged after the call.  In other words, after `feupdateenv'
     is called, the status word is the bitwise OR of the previous
     status word and the one saved in ENVP.

     The function returns zero in case the operation was successful, a
     non-zero value otherwise.

To control for individual exceptions if raising them causes a trap to
occur, you can use the following two functions.

   *Portability Note:* These functions are all GNU extensions.

 -- Function: int feenableexcept (int EXCEPTS)
     This functions enables traps for each of the exceptions as
     indicated by the parameter EXCEPT.  The individual excepetions are
     described in *Note Status bit operations::.  Only the specified
     exceptions are enabled, the status of the other exceptions is not
     changed.

     The function returns the previous enabled exceptions in case the
     operation was successful, `-1' otherwise.

 -- Function: int fedisableexcept (int EXCEPTS)
     This functions disables traps for each of the exceptions as
     indicated by the parameter EXCEPT.  The individual excepetions are
     described in *Note Status bit operations::.  Only the specified
     exceptions are disabled, the status of the other exceptions is not
     changed.

     The function returns the previous enabled exceptions in case the
     operation was successful, `-1' otherwise.

 -- Function: int fegetexcept (int EXCEPTS)
     The function returns a bitmask of all currently enabled
     exceptions.  It returns `-1' in case of failure.


File: libc.info,  Node: Arithmetic Functions,  Next: Complex Numbers,  Prev: Control Functions,  Up: Arithmetic

20.8 Arithmetic Functions
=========================

The C library provides functions to do basic operations on
floating-point numbers.  These include absolute value, maximum and
minimum, normalization, bit twiddling, rounding, and a few others.

* Menu:

* Absolute Value::              Absolute values of integers and floats.
* Normalization Functions::     Extracting exponents and putting them back.
* Rounding Functions::          Rounding floats to integers.
* Remainder Functions::         Remainders on division, precisely defined.
* FP Bit Twiddling::            Sign bit adjustment.  Adding epsilon.
* FP Comparison Functions::     Comparisons without risk of exceptions.
* Misc FP Arithmetic::          Max, min, positive difference, multiply-add.


File: libc.info,  Node: Absolute Value,  Next: Normalization Functions,  Up: Arithmetic Functions

20.8.1 Absolute Value
---------------------

These functions are provided for obtaining the "absolute value" (or
"magnitude") of a number.  The absolute value of a real number X is X
if X is positive, -X if X is negative.  For a complex number Z, whose
real part is X and whose imaginary part is Y, the absolute value is
`sqrt (X*X + Y*Y)'.

   Prototypes for `abs', `labs' and `llabs' are in `stdlib.h';
`imaxabs' is declared in `inttypes.h'; `fabs', `fabsf' and `fabsl' are
declared in `math.h'.  `cabs', `cabsf' and `cabsl' are declared in
`complex.h'.

 -- Function: int abs (int NUMBER)
 -- Function: long int labs (long int NUMBER)
 -- Function: long long int llabs (long long int NUMBER)
 -- Function: intmax_t imaxabs (intmax_t NUMBER)
     These functions return the absolute value of NUMBER.

     Most computers use a two's complement integer representation, in
     which the absolute value of `INT_MIN' (the smallest possible `int')
     cannot be represented; thus, `abs (INT_MIN)' is not defined.

     `llabs' and `imaxdiv' are new to ISO C99.

     See *Note Integers:: for a description of the `intmax_t' type.


 -- Function: double fabs (double NUMBER)
 -- Function: float fabsf (float NUMBER)
 -- Function: long double fabsl (long double NUMBER)
     This function returns the absolute value of the floating-point
     number NUMBER.

 -- Function: double cabs (complex double Z)
 -- Function: float cabsf (complex float Z)
 -- Function: long double cabsl (complex long double Z)
     These functions return the absolute  value of the complex number Z
     (*note Complex Numbers::).  The absolute value of a complex number
     is:

          sqrt (creal (Z) * creal (Z) + cimag (Z) * cimag (Z))

     This function should always be used instead of the direct formula
     because it takes special care to avoid losing precision.  It may
     also take advantage of hardware support for this operation. See
     `hypot' in *Note Exponents and Logarithms::.


File: libc.info,  Node: Normalization Functions,  Next: Rounding Functions,  Prev: Absolute Value,  Up: Arithmetic Functions

20.8.2 Normalization Functions
------------------------------

The functions described in this section are primarily provided as a way
to efficiently perform certain low-level manipulations on floating point
numbers that are represented internally using a binary radix; see *Note
Floating Point Concepts::.  These functions are required to have
equivalent behavior even if the representation does not use a radix of
2, but of course they are unlikely to be particularly efficient in
those cases.

   All these functions are declared in `math.h'.

 -- Function: double frexp (double VALUE, int *EXPONENT)
 -- Function: float frexpf (float VALUE, int *EXPONENT)
 -- Function: long double frexpl (long double VALUE, int *EXPONENT)
     These functions are used to split the number VALUE into a
     normalized fraction and an exponent.

     If the argument VALUE is not zero, the return value is VALUE times
     a power of two, and is always in the range 1/2 (inclusive) to 1
     (exclusive).  The corresponding exponent is stored in `*EXPONENT';
     the return value multiplied by 2 raised to this exponent equals
     the original number VALUE.

     For example, `frexp (12.8, &exponent)' returns `0.8' and stores
     `4' in `exponent'.

     If VALUE is zero, then the return value is zero and zero is stored
     in `*EXPONENT'.

 -- Function: double ldexp (double VALUE, int EXPONENT)
 -- Function: float ldexpf (float VALUE, int EXPONENT)
 -- Function: long double ldexpl (long double VALUE, int EXPONENT)
     These functions return the result of multiplying the floating-point
     number VALUE by 2 raised to the power EXPONENT.  (It can be used
     to reassemble floating-point numbers that were taken apart by
     `frexp'.)

     For example, `ldexp (0.8, 4)' returns `12.8'.

   The following functions, which come from BSD, provide facilities
equivalent to those of `ldexp' and `frexp'.  See also the ISO C
function `logb' which originally also appeared in BSD.

 -- Function: double scalb (double VALUE, int EXPONENT)
 -- Function: float scalbf (float VALUE, int EXPONENT)
 -- Function: long double scalbl (long double VALUE, int EXPONENT)
     The `scalb' function is the BSD name for `ldexp'.

 -- Function: long long int scalbn (double X, int n)
 -- Function: long long int scalbnf (float X, int n)
 -- Function: long long int scalbnl (long double X, int n)
     `scalbn' is identical to `scalb', except that the exponent N is an
     `int' instead of a floating-point number.

 -- Function: long long int scalbln (double X, long int n)
 -- Function: long long int scalblnf (float X, long int n)
 -- Function: long long int scalblnl (long double X, long int n)
     `scalbln' is identical to `scalb', except that the exponent N is a
     `long int' instead of a floating-point number.

 -- Function: long long int significand (double X)
 -- Function: long long int significandf (float X)
 -- Function: long long int significandl (long double X)
     `significand' returns the mantissa of X scaled to the range [1, 2).
     It is equivalent to `scalb (X, (double) -ilogb (X))'.

     This function exists mainly for use in certain standardized tests
     of IEEE 754 conformance.


File: libc.info,  Node: Rounding Functions,  Next: Remainder Functions,  Prev: Normalization Functions,  Up: Arithmetic Functions

20.8.3 Rounding Functions
-------------------------

The functions listed here perform operations such as rounding and
truncation of floating-point values. Some of these functions convert
floating point numbers to integer values.  They are all declared in
`math.h'.

   You can also convert floating-point numbers to integers simply by
casting them to `int'.  This discards the fractional part, effectively
rounding towards zero.  However, this only works if the result can
actually be represented as an `int'--for very large numbers, this is
impossible.  The functions listed here return the result as a `double'
instead to get around this problem.

 -- Function: double ceil (double X)
 -- Function: float ceilf (float X)
 -- Function: long double ceill (long double X)
     These functions round X upwards to the nearest integer, returning
     that value as a `double'.  Thus, `ceil (1.5)' is `2.0'.

 -- Function: double floor (double X)
 -- Function: float floorf (float X)
 -- Function: long double floorl (long double X)
     These functions round X downwards to the nearest integer,
     returning that value as a `double'.  Thus, `floor (1.5)' is `1.0'
     and `floor (-1.5)' is `-2.0'.

 -- Function: double trunc (double X)
 -- Function: float truncf (float X)
 -- Function: long double truncl (long double X)
     The `trunc' functions round X towards zero to the nearest integer
     (returned in floating-point format).  Thus, `trunc (1.5)' is `1.0'
     and `trunc (-1.5)' is `-1.0'.

 -- Function: double rint (double X)
 -- Function: float rintf (float X)
 -- Function: long double rintl (long double X)
     These functions round X to an integer value according to the
     current rounding mode.  *Note Floating Point Parameters::, for
     information about the various rounding modes.  The default
     rounding mode is to round to the nearest integer; some machines
     support other modes, but round-to-nearest is always used unless
     you explicitly select another.

     If X was not initially an integer, these functions raise the
     inexact exception.

 -- Function: double nearbyint (double X)
 -- Function: float nearbyintf (float X)
 -- Function: long double nearbyintl (long double X)
     These functions return the same value as the `rint' functions, but
     do not raise the inexact exception if X is not an integer.

 -- Function: double round (double X)
 -- Function: float roundf (float X)
 -- Function: long double roundl (long double X)
     These functions are similar to `rint', but they round halfway
     cases away from zero instead of to the nearest even integer.

 -- Function: long int lrint (double X)
 -- Function: long int lrintf (float X)
 -- Function: long int lrintl (long double X)
     These functions are just like `rint', but they return a `long int'
     instead of a floating-point number.

 -- Function: long long int llrint (double X)
 -- Function: long long int llrintf (float X)
 -- Function: long long int llrintl (long double X)
     These functions are just like `rint', but they return a `long long
     int' instead of a floating-point number.

 -- Function: long int lround (double X)
 -- Function: long int lroundf (float X)
 -- Function: long int lroundl (long double X)
     These functions are just like `round', but they return a `long
     int' instead of a floating-point number.

 -- Function: long long int llround (double X)
 -- Function: long long int llroundf (float X)
 -- Function: long long int llroundl (long double X)
     These functions are just like `round', but they return a `long
     long int' instead of a floating-point number.

 -- Function: double modf (double VALUE, double *INTEGER-PART)
 -- Function: float modff (float VALUE, float *INTEGER-PART)
 -- Function: long double modfl (long double VALUE, long double
          *INTEGER-PART)
     These functions break the argument VALUE into an integer part and a
     fractional part (between `-1' and `1', exclusive).  Their sum
     equals VALUE.  Each of the parts has the same sign as VALUE, and
     the integer part is always rounded toward zero.

     `modf' stores the integer part in `*INTEGER-PART', and returns the
     fractional part.  For example, `modf (2.5, &intpart)' returns
     `0.5' and stores `2.0' into `intpart'.


File: libc.info,  Node: Remainder Functions,  Next: FP Bit Twiddling,  Prev: Rounding Functions,  Up: Arithmetic Functions

20.8.4 Remainder Functions
--------------------------

The functions in this section compute the remainder on division of two
floating-point numbers.  Each is a little different; pick the one that
suits your problem.

 -- Function: double fmod (double NUMERATOR, double DENOMINATOR)
 -- Function: float fmodf (float NUMERATOR, float DENOMINATOR)
 -- Function: long double fmodl (long double NUMERATOR, long double
          DENOMINATOR)
     These functions compute the remainder from the division of
     NUMERATOR by DENOMINATOR.  Specifically, the return value is
     `NUMERATOR - N * DENOMINATOR', where N is the quotient of
     NUMERATOR divided by DENOMINATOR, rounded towards zero to an
     integer.  Thus, `fmod (6.5, 2.3)' returns `1.9', which is `6.5'
     minus `4.6'.

     The result has the same sign as the NUMERATOR and has magnitude
     less than the magnitude of the DENOMINATOR.

     If DENOMINATOR is zero, `fmod' signals a domain error.

 -- Function: double drem (double NUMERATOR, double DENOMINATOR)
 -- Function: float dremf (float NUMERATOR, float DENOMINATOR)
 -- Function: long double dreml (long double NUMERATOR, long double
          DENOMINATOR)
     These functions are like `fmod' except that they rounds the
     internal quotient N to the nearest integer instead of towards zero
     to an integer.  For example, `drem (6.5, 2.3)' returns `-0.4',
     which is `6.5' minus `6.9'.

     The absolute value of the result is less than or equal to half the
     absolute value of the DENOMINATOR.  The difference between `fmod
     (NUMERATOR, DENOMINATOR)' and `drem (NUMERATOR, DENOMINATOR)' is
     always either DENOMINATOR, minus DENOMINATOR, or zero.

     If DENOMINATOR is zero, `drem' signals a domain error.

 -- Function: double remainder (double NUMERATOR, double DENOMINATOR)
 -- Function: float remainderf (float NUMERATOR, float DENOMINATOR)
 -- Function: long double remainderl (long double NUMERATOR, long
          double DENOMINATOR)
     This function is another name for `drem'.


File: libc.info,  Node: FP Bit Twiddling,  Next: FP Comparison Functions,  Prev: Remainder Functions,  Up: Arithmetic Functions

20.8.5 Setting and modifying single bits of FP values
-----------------------------------------------------

There are some operations that are too complicated or expensive to
perform by hand on floating-point numbers.  ISO C99 defines functions
to do these operations, which mostly involve changing single bits.

 -- Function: double copysign (double X, double Y)
 -- Function: float copysignf (float X, float Y)
 -- Function: long double copysignl (long double X, long double Y)
     These functions return X but with the sign of Y.  They work even
     if X or Y are NaN or zero.  Both of these can carry a sign
     (although not all implementations support it) and this is one of
     the few operations that can tell the difference.

     `copysign' never raises an exception.

     This function is defined in IEC 559 (and the appendix with
     recommended functions in IEEE 754/IEEE 854).

 -- Function: int signbit (_float-type_ X)
     `signbit' is a generic macro which can work on all floating-point
     types.  It returns a nonzero value if the value of X has its sign
     bit set.

     This is not the same as `x < 0.0', because IEEE 754 floating point
     allows zero to be signed.  The comparison `-0.0 < 0.0' is false,
     but `signbit (-0.0)' will return a nonzero value.

 -- Function: double nextafter (double X, double Y)
 -- Function: float nextafterf (float X, float Y)
 -- Function: long double nextafterl (long double X, long double Y)
     The `nextafter' function returns the next representable neighbor of
     X in the direction towards Y.  The size of the step between X and
     the result depends on the type of the result.  If X = Y the
     function simply returns Y.  If either value is `NaN', `NaN' is
     returned.  Otherwise a value corresponding to the value of the
     least significant bit in the mantissa is added or subtracted,
     depending on the direction.  `nextafter' will signal overflow or
     underflow if the result goes outside of the range of normalized
     numbers.

     This function is defined in IEC 559 (and the appendix with
     recommended functions in IEEE 754/IEEE 854).

 -- Function: double nexttoward (double X, long double Y)
 -- Function: float nexttowardf (float X, long double Y)
 -- Function: long double nexttowardl (long double X, long double Y)
     These functions are identical to the corresponding versions of
     `nextafter' except that their second argument is a `long double'.

 -- Function: double nan (const char *TAGP)
 -- Function: float nanf (const char *TAGP)
 -- Function: long double nanl (const char *TAGP)
     The `nan' function returns a representation of NaN, provided that
     NaN is supported by the target platform.  `nan
     ("N-CHAR-SEQUENCE")' is equivalent to `strtod
     ("NAN(N-CHAR-SEQUENCE)")'.

     The argument TAGP is used in an unspecified manner.  On IEEE 754
     systems, there are many representations of NaN, and TAGP selects
     one.  On other systems it may do nothing.


File: libc.info,  Node: FP Comparison Functions,  Next: Misc FP Arithmetic,  Prev: FP Bit Twiddling,  Up: Arithmetic Functions

20.8.6 Floating-Point Comparison Functions
------------------------------------------

The standard C comparison operators provoke exceptions when one or other
of the operands is NaN.  For example,

     int v = a < 1.0;

will raise an exception if A is NaN.  (This does _not_ happen with `=='
and `!='; those merely return false and true, respectively, when NaN is
examined.)  Frequently this exception is undesirable.  ISO C99
therefore defines comparison functions that do not raise exceptions
when NaN is examined.  All of the functions are implemented as macros
which allow their arguments to be of any floating-point type.  The
macros are guaranteed to evaluate their arguments only once.

 -- Macro: int isgreater (_real-floating_ X, _real-floating_ Y)
     This macro determines whether the argument X is greater than Y.
     It is equivalent to `(X) > (Y)', but no exception is raised if X
     or Y are NaN.

 -- Macro: int isgreaterequal (_real-floating_ X, _real-floating_ Y)
     This macro determines whether the argument X is greater than or
     equal to Y.  It is equivalent to `(X) >= (Y)', but no exception is
     raised if X or Y are NaN.

 -- Macro: int isless (_real-floating_ X, _real-floating_ Y)
     This macro determines whether the argument X is less than Y.  It
     is equivalent to `(X) < (Y)', but no exception is raised if X or Y
     are NaN.

 -- Macro: int islessequal (_real-floating_ X, _real-floating_ Y)
     This macro determines whether the argument X is less than or equal
     to Y.  It is equivalent to `(X) <= (Y)', but no exception is
     raised if X or Y are NaN.

 -- Macro: int islessgreater (_real-floating_ X, _real-floating_ Y)
     This macro determines whether the argument X is less or greater
     than Y.  It is equivalent to `(X) < (Y) || (X) > (Y)' (although it
     only evaluates X and Y once), but no exception is raised if X or Y
     are NaN.

     This macro is not equivalent to `X != Y', because that expression
     is true if X or Y are NaN.

 -- Macro: int isunordered (_real-floating_ X, _real-floating_ Y)
     This macro determines whether its arguments are unordered.  In
     other words, it is true if X or Y are NaN, and false otherwise.

   Not all machines provide hardware support for these operations.  On
machines that don't, the macros can be very slow.  Therefore, you should
not use these functions when NaN is not a concern.

   *Note_* There are no macros `isequal' or `isunequal'.  They are
unnecessary, because the `==' and `!=' operators do _not_ throw an
exception if one or both of the operands are NaN.


File: libc.info,  Node: Misc FP Arithmetic,  Prev: FP Comparison Functions,  Up: Arithmetic Functions

20.8.7 Miscellaneous FP arithmetic functions
--------------------------------------------

The functions in this section perform miscellaneous but common
operations that are awkward to express with C operators.  On some
processors these functions can use special machine instructions to
perform these operations faster than the equivalent C code.

 -- Function: double fmin (double X, double Y)
 -- Function: float fminf (float X, float Y)
 -- Function: long double fminl (long double X, long double Y)
     The `fmin' function returns the lesser of the two values X and Y.
     It is similar to the expression
          ((x) < (y) ? (x) : (y))
     except that X and Y are only evaluated once.

     If an argument is NaN, the other argument is returned.  If both
     arguments are NaN, NaN is returned.

 -- Function: double fmax (double X, double Y)
 -- Function: float fmaxf (float X, float Y)
 -- Function: long double fmaxl (long double X, long double Y)
     The `fmax' function returns the greater of the two values X and Y.

     If an argument is NaN, the other argument is returned.  If both
     arguments are NaN, NaN is returned.

 -- Function: double fdim (double X, double Y)
 -- Function: float fdimf (float X, float Y)
 -- Function: long double fdiml (long double X, long double Y)
     The `fdim' function returns the positive difference between X and
     Y.  The positive difference is X - Y if X is greater than Y, and 0
     otherwise.

     If X, Y, or both are NaN, NaN is returned.

 -- Function: double fma (double X, double Y, double Z)
 -- Function: float fmaf (float X, float Y, float Z)
 -- Function: long double fmal (long double X, long double Y, long
          double Z)
     The `fma' function performs floating-point multiply-add.  This is
     the operation (X * Y) + Z, but the intermediate result is not
     rounded to the destination type.  This can sometimes improve the
     precision of a calculation.

     This function was introduced because some processors have a special
     instruction to perform multiply-add.  The C compiler cannot use it
     directly, because the expression `x*y + z' is defined to round the
     intermediate result.  `fma' lets you choose when you want to round
     only once.

     On processors which do not implement multiply-add in hardware,
     `fma' can be very slow since it must avoid intermediate rounding.
     `math.h' defines the symbols `FP_FAST_FMA', `FP_FAST_FMAF', and
     `FP_FAST_FMAL' when the corresponding version of `fma' is no
     slower than the expression `x*y + z'.  In the GNU C library, this
     always means the operation is implemented in hardware.


File: libc.info,  Node: Complex Numbers,  Next: Operations on Complex,  Prev: Arithmetic Functions,  Up: Arithmetic

20.9 Complex Numbers
====================

ISO C99 introduces support for complex numbers in C.  This is done with
a new type qualifier, `complex'.  It is a keyword if and only if
`complex.h' has been included.  There are three complex types,
corresponding to the three real types:  `float complex', `double
complex', and `long double complex'.

   To construct complex numbers you need a way to indicate the imaginary
part of a number.  There is no standard notation for an imaginary
floating point constant.  Instead, `complex.h' defines two macros that
can be used to create complex numbers.

 -- Macro: const float complex _Complex_I
     This macro is a representation of the complex number "0+1i".
     Multiplying a real floating-point value by `_Complex_I' gives a
     complex number whose value is purely imaginary.  You can use this
     to construct complex constants:

          3.0 + 4.0i = `3.0 + 4.0 * _Complex_I'

     Note that `_Complex_I * _Complex_I' has the value `-1', but the
     type of that value is `complex'.

`_Complex_I' is a bit of a mouthful.  `complex.h' also defines a
shorter name for the same constant.

 -- Macro: const float complex I
     This macro has exactly the same value as `_Complex_I'.  Most of the
     time it is preferable.  However, it causes problems if you want to
     use the identifier `I' for something else.  You can safely write

          #include <complex.h>
          #undef I

     if you need `I' for your own purposes.  (In that case we recommend
     you also define some other short name for `_Complex_I', such as
     `J'.)



File: libc.info,  Node: Operations on Complex,  Next: Parsing of Numbers,  Prev: Complex Numbers,  Up: Arithmetic

20.10 Projections, Conjugates, and Decomposing of Complex Numbers
=================================================================

ISO C99 also defines functions that perform basic operations on complex
numbers, such as decomposition and conjugation.  The prototypes for all
these functions are in `complex.h'.  All functions are available in
three variants, one for each of the three complex types.

 -- Function: double creal (complex double Z)
 -- Function: float crealf (complex float Z)
 -- Function: long double creall (complex long double Z)
     These functions return the real part of the complex number Z.

 -- Function: double cimag (complex double Z)
 -- Function: float cimagf (complex float Z)
 -- Function: long double cimagl (complex long double Z)
     These functions return the imaginary part of the complex number Z.

 -- Function: complex double conj (complex double Z)
 -- Function: complex float conjf (complex float Z)
 -- Function: complex long double conjl (complex long double Z)
     These functions return the conjugate value of the complex number
     Z.  The conjugate of a complex number has the same real part and a
     negated imaginary part.  In other words, `conj(a + bi) = a + -bi'.

 -- Function: double carg (complex double Z)
 -- Function: float cargf (complex float Z)
 -- Function: long double cargl (complex long double Z)
     These functions return the argument of the complex number Z.  The
     argument of a complex number is the angle in the complex plane
     between the positive real axis and a line passing through zero and
     the number.  This angle is measured in the usual fashion and
     ranges from 0 to 2pi.

     `carg' has a branch cut along the positive real axis.

 -- Function: complex double cproj (complex double Z)
 -- Function: complex float cprojf (complex float Z)
 -- Function: complex long double cprojl (complex long double Z)
     These functions return the projection of the complex value Z onto
     the Riemann sphere.  Values with a infinite imaginary part are
     projected to positive infinity on the real axis, even if the real
     part is NaN.  If the real part is infinite, the result is
     equivalent to

          INFINITY + I * copysign (0.0, cimag (z))


File: libc.info,  Node: Parsing of Numbers,  Next: System V Number Conversion,  Prev: Operations on Complex,  Up: Arithmetic

20.11 Parsing of Numbers
========================

This section describes functions for "reading" integer and
floating-point numbers from a string.  It may be more convenient in some
cases to use `sscanf' or one of the related functions; see *Note
Formatted Input::.  But often you can make a program more robust by
finding the tokens in the string by hand, then converting the numbers
one by one.

* Menu:

* Parsing of Integers::         Functions for conversion of integer values.
* Parsing of Floats::           Functions for conversion of floating-point
				 values.


File: libc.info,  Node: Parsing of Integers,  Next: Parsing of Floats,  Up: Parsing of Numbers

20.11.1 Parsing of Integers
---------------------------

The `str' functions are declared in `stdlib.h' and those beginning with
`wcs' are declared in `wchar.h'.  One might wonder about the use of
`restrict' in the prototypes of the functions in this section.  It is
seemingly useless but the ISO C standard uses it (for the functions
defined there) so we have to do it as well.

 -- Function: long int strtol (const char *restrict STRING, char
          **restrict TAILPTR, int BASE)
     The `strtol' ("string-to-long") function converts the initial part
     of STRING to a signed integer, which is returned as a value of
     type `long int'.

     This function attempts to decompose STRING as follows:

        * A (possibly empty) sequence of whitespace characters.  Which
          characters are whitespace is determined by the `isspace'
          function (*note Classification of Characters::).  These are
          discarded.

        * An optional plus or minus sign (`+' or `-').

        * A nonempty sequence of digits in the radix specified by BASE.

          If BASE is zero, decimal radix is assumed unless the series of
          digits begins with `0' (specifying octal radix), or `0x' or
          `0X' (specifying hexadecimal radix); in other words, the same
          syntax used for integer constants in C.

          Otherwise BASE must have a value between `2' and `36'.  If
          BASE is `16', the digits may optionally be preceded by `0x'
          or `0X'.  If base has no legal value the value returned is
          `0l' and the global variable `errno' is set to `EINVAL'.

        * Any remaining characters in the string.  If TAILPTR is not a
          null pointer, `strtol' stores a pointer to this tail in
          `*TAILPTR'.

     If the string is empty, contains only whitespace, or does not
     contain an initial substring that has the expected syntax for an
     integer in the specified BASE, no conversion is performed.  In
     this case, `strtol' returns a value of zero and the value stored in
     `*TAILPTR' is the value of STRING.

     In a locale other than the standard `"C"' locale, this function
     may recognize additional implementation-dependent syntax.

     If the string has valid syntax for an integer but the value is not
     representable because of overflow, `strtol' returns either
     `LONG_MAX' or `LONG_MIN' (*note Range of Type::), as appropriate
     for the sign of the value.  It also sets `errno' to `ERANGE' to
     indicate there was overflow.

     You should not check for errors by examining the return value of
     `strtol', because the string might be a valid representation of
     `0l', `LONG_MAX', or `LONG_MIN'.  Instead, check whether TAILPTR
     points to what you expect after the number (e.g. `'\0'' if the
     string should end after the number).  You also need to clear ERRNO
     before the call and check it afterward, in case there was overflow.

     There is an example at the end of this section.

 -- Function: long int wcstol (const wchar_t *restrict STRING, wchar_t
          **restrict TAILPTR, int BASE)
     The `wcstol' function is equivalent to the `strtol' function in
     nearly all aspects but handles wide character strings.

     The `wcstol' function was introduced in Amendment 1 of ISO C90.

 -- Function: unsigned long int strtoul (const char *retrict STRING,
          char **restrict TAILPTR, int BASE)
     The `strtoul' ("string-to-unsigned-long") function is like
     `strtol' except it converts to an `unsigned long int' value.  The
     syntax is the same as described above for `strtol'.  The value
     returned on overflow is `ULONG_MAX' (*note Range of Type::).

     If STRING depicts a negative number, `strtoul' acts the same as
     STRTOL but casts the result to an unsigned integer.  That means
     for example that `strtoul' on `"-1"' returns `ULONG_MAX' and an
     input more negative than `LONG_MIN' returns (`ULONG_MAX' + 1) / 2.

     `strtoul' sets ERRNO to `EINVAL' if BASE is out of range, or
     `ERANGE' on overflow.

 -- Function: unsigned long int wcstoul (const wchar_t *restrict
          STRING, wchar_t **restrict TAILPTR, int BASE)
     The `wcstoul' function is equivalent to the `strtoul' function in
     nearly all aspects but handles wide character strings.

     The `wcstoul' function was introduced in Amendment 1 of ISO C90.

 -- Function: long long int strtoll (const char *restrict STRING, char
          **restrict TAILPTR, int BASE)
     The `strtoll' function is like `strtol' except that it returns a
     `long long int' value, and accepts numbers with a correspondingly
     larger range.

     If the string has valid syntax for an integer but the value is not
     representable because of overflow, `strtoll' returns either
     `LONG_LONG_MAX' or `LONG_LONG_MIN' (*note Range of Type::), as
     appropriate for the sign of the value.  It also sets `errno' to
     `ERANGE' to indicate there was overflow.

     The `strtoll' function was introduced in ISO C99.

 -- Function: long long int wcstoll (const wchar_t *restrict STRING,
          wchar_t **restrict TAILPTR, int BASE)
     The `wcstoll' function is equivalent to the `strtoll' function in
     nearly all aspects but handles wide character strings.

     The `wcstoll' function was introduced in Amendment 1 of ISO C90.

 -- Function: long long int strtoq (const char *restrict STRING, char
          **restrict TAILPTR, int BASE)
     `strtoq' ("string-to-quad-word") is the BSD name for `strtoll'.

 -- Function: long long int wcstoq (const wchar_t *restrict STRING,
          wchar_t **restrict TAILPTR, int BASE)
     The `wcstoq' function is equivalent to the `strtoq' function in
     nearly all aspects but handles wide character strings.

     The `wcstoq' function is a GNU extension.

 -- Function: unsigned long long int strtoull (const char *restrict
          STRING, char **restrict TAILPTR, int BASE)
     The `strtoull' function is related to `strtoll' the same way
     `strtoul' is related to `strtol'.

     The `strtoull' function was introduced in ISO C99.

 -- Function: unsigned long long int wcstoull (const wchar_t *restrict
          STRING, wchar_t **restrict TAILPTR, int BASE)
     The `wcstoull' function is equivalent to the `strtoull' function
     in nearly all aspects but handles wide character strings.

     The `wcstoull' function was introduced in Amendment 1 of ISO C90.

 -- Function: unsigned long long int strtouq (const char *restrict
          STRING, char **restrict TAILPTR, int BASE)
     `strtouq' is the BSD name for `strtoull'.

 -- Function: unsigned long long int wcstouq (const wchar_t *restrict
          STRING, wchar_t **restrict TAILPTR, int BASE)
     The `wcstouq' function is equivalent to the `strtouq' function in
     nearly all aspects but handles wide character strings.

     The `wcstouq' function is a GNU extension.

 -- Function: intmax_t strtoimax (const char *restrict STRING, char
          **restrict TAILPTR, int BASE)
     The `strtoimax' function is like `strtol' except that it returns a
     `intmax_t' value, and accepts numbers of a corresponding range.

     If the string has valid syntax for an integer but the value is not
     representable because of overflow, `strtoimax' returns either
     `INTMAX_MAX' or `INTMAX_MIN' (*note Integers::), as appropriate
     for the sign of the value.  It also sets `errno' to `ERANGE' to
     indicate there was overflow.

     See *Note Integers:: for a description of the `intmax_t' type.  The
     `strtoimax' function was introduced in ISO C99.

 -- Function: intmax_t wcstoimax (const wchar_t *restrict STRING,
          wchar_t **restrict TAILPTR, int BASE)
     The `wcstoimax' function is equivalent to the `strtoimax' function
     in nearly all aspects but handles wide character strings.

     The `wcstoimax' function was introduced in ISO C99.

 -- Function: uintmax_t strtoumax (const char *restrict STRING, char
          **restrict TAILPTR, int BASE)
     The `strtoumax' function is related to `strtoimax' the same way
     that `strtoul' is related to `strtol'.

     See *Note Integers:: for a description of the `intmax_t' type.  The
     `strtoumax' function was introduced in ISO C99.

 -- Function: uintmax_t wcstoumax (const wchar_t *restrict STRING,
          wchar_t **restrict TAILPTR, int BASE)
     The `wcstoumax' function is equivalent to the `strtoumax' function
     in nearly all aspects but handles wide character strings.

     The `wcstoumax' function was introduced in ISO C99.

 -- Function: long int atol (const char *STRING)
     This function is similar to the `strtol' function with a BASE
     argument of `10', except that it need not detect overflow errors.
     The `atol' function is provided mostly for compatibility with
     existing code; using `strtol' is more robust.

 -- Function: int atoi (const char *STRING)
     This function is like `atol', except that it returns an `int'.
     The `atoi' function is also considered obsolete; use `strtol'
     instead.

 -- Function: long long int atoll (const char *STRING)
     This function is similar to `atol', except it returns a `long long
     int'.

     The `atoll' function was introduced in ISO C99.  It too is
     obsolete (despite having just been added); use `strtoll' instead.

   All the functions mentioned in this section so far do not handle
alternative representations of characters as described in the locale
data.  Some locales specify thousands separator and the way they have to
be used which can help to make large numbers more readable.  To read
such numbers one has to use the `scanf' functions with the `'' flag.

   Here is a function which parses a string as a sequence of integers
and returns the sum of them:

     int
     sum_ints_from_string (char *string)
     {
       int sum = 0;

       while (1) {
         char *tail;
         int next;

         /* Skip whitespace by hand, to detect the end.  */
         while (isspace (*string)) string++;
         if (*string == 0)
           break;

         /* There is more nonwhitespace,  */
         /* so it ought to be another number.  */
         errno = 0;
         /* Parse it.  */
         next = strtol (string, &tail, 0);
         /* Add it in, if not overflow.  */
         if (errno)
           printf ("Overflow\n");
         else
           sum += next;
         /* Advance past it.  */
         string = tail;
       }

       return sum;
     }


File: libc.info,  Node: Parsing of Floats,  Prev: Parsing of Integers,  Up: Parsing of Numbers

20.11.2 Parsing of Floats
-------------------------

The `str' functions are declared in `stdlib.h' and those beginning with
`wcs' are declared in `wchar.h'.  One might wonder about the use of
`restrict' in the prototypes of the functions in this section.  It is
seemingly useless but the ISO C standard uses it (for the functions
defined there) so we have to do it as well.

 -- Function: double strtod (const char *restrict STRING, char
          **restrict TAILPTR)
     The `strtod' ("string-to-double") function converts the initial
     part of STRING to a floating-point number, which is returned as a
     value of type `double'.

     This function attempts to decompose STRING as follows:

        * A (possibly empty) sequence of whitespace characters.  Which
          characters are whitespace is determined by the `isspace'
          function (*note Classification of Characters::).  These are
          discarded.

        * An optional plus or minus sign (`+' or `-').

        * A floating point number in decimal or hexadecimal format.  The
          decimal format is:
             - A nonempty sequence of digits optionally containing a
               decimal-point character--normally `.', but it depends on
               the locale (*note General Numeric::).

             - An optional exponent part, consisting of a character `e'
               or `E', an optional sign, and a sequence of digits.


          The hexadecimal format is as follows:
             - A 0x or 0X followed by a nonempty sequence of
               hexadecimal digits optionally containing a decimal-point
               character--normally `.', but it depends on the locale
               (*note General Numeric::).

             - An optional binary-exponent part, consisting of a
               character `p' or `P', an optional sign, and a sequence
               of digits.


        * Any remaining characters in the string.  If TAILPTR is not a
          null pointer, a pointer to this tail of the string is stored
          in `*TAILPTR'.

     If the string is empty, contains only whitespace, or does not
     contain an initial substring that has the expected syntax for a
     floating-point number, no conversion is performed.  In this case,
     `strtod' returns a value of zero and the value returned in
     `*TAILPTR' is the value of STRING.

     In a locale other than the standard `"C"' or `"POSIX"' locales,
     this function may recognize additional locale-dependent syntax.

     If the string has valid syntax for a floating-point number but the
     value is outside the range of a `double', `strtod' will signal
     overflow or underflow as described in *Note Math Error Reporting::.

     `strtod' recognizes four special input strings.  The strings
     `"inf"' and `"infinity"' are converted to oo, or to the largest
     representable value if the floating-point format doesn't support
     infinities.  You can prepend a `"+"' or `"-"' to specify the sign.
     Case is ignored when scanning these strings.

     The strings `"nan"' and `"nan(CHARS...)"' are converted to NaN.
     Again, case is ignored.  If CHARS... are provided, they are used
     in some unspecified fashion to select a particular representation
     of NaN (there can be several).

     Since zero is a valid result as well as the value returned on
     error, you should check for errors in the same way as for
     `strtol', by examining ERRNO and TAILPTR.

 -- Function: float strtof (const char *STRING, char **TAILPTR)
 -- Function: long double strtold (const char *STRING, char **TAILPTR)
     These functions are analogous to `strtod', but return `float' and
     `long double' values respectively.  They report errors in the same
     way as `strtod'.  `strtof' can be substantially faster than
     `strtod', but has less precision; conversely, `strtold' can be
     much slower but has more precision (on systems where `long double'
     is a separate type).

     These functions have been GNU extensions and are new to ISO C99.

 -- Function: double wcstod (const wchar_t *restrict STRING, wchar_t
          **restrict TAILPTR)
 -- Function: float wcstof (const wchar_t *STRING, wchar_t **TAILPTR)
 -- Function: long double wcstold (const wchar_t *STRING, wchar_t
          **TAILPTR)
     The `wcstod', `wcstof', and `wcstol' functions are equivalent in
     nearly all aspect to the `strtod', `strtof', and `strtold'
     functions but it handles wide character string.

     The `wcstod' function was introduced in Amendment 1 of ISO C90.
     The `wcstof' and `wcstold' functions were introduced in ISO C99.

 -- Function: double atof (const char *STRING)
     This function is similar to the `strtod' function, except that it
     need not detect overflow and underflow errors.  The `atof' function
     is provided mostly for compatibility with existing code; using
     `strtod' is more robust.

   The GNU C library also provides `_l' versions of these functions,
which take an additional argument, the locale to use in conversion.
*Note Parsing of Integers::.


File: libc.info,  Node: System V Number Conversion,  Prev: Parsing of Numbers,  Up: Arithmetic

20.12 Old-fashioned System V number-to-string functions
=======================================================

The old System V C library provided three functions to convert numbers
to strings, with unusual and hard-to-use semantics.  The GNU C library
also provides these functions and some natural extensions.

   These functions are only available in glibc and on systems descended
from AT&T Unix.  Therefore, unless these functions do precisely what you
need, it is better to use `sprintf', which is standard.

   All these functions are defined in `stdlib.h'.

 -- Function: char * ecvt (double VALUE, int NDIGIT, int *DECPT, int
          *NEG)
     The function `ecvt' converts the floating-point number VALUE to a
     string with at most NDIGIT decimal digits.  The returned string
     contains no decimal point or sign. The first digit of the string
     is non-zero (unless VALUE is actually zero) and the last digit is
     rounded to nearest.  `*DECPT' is set to the index in the string of
     the first digit after the decimal point.  `*NEG' is set to a
     nonzero value if VALUE is negative, zero otherwise.

     If NDIGIT decimal digits would exceed the precision of a `double'
     it is reduced to a system-specific value.

     The returned string is statically allocated and overwritten by
     each call to `ecvt'.

     If VALUE is zero, it is implementation defined whether `*DECPT' is
     `0' or `1'.

     For example: `ecvt (12.3, 5, &d, &n)' returns `"12300"' and sets D
     to `2' and N to `0'.

 -- Function: char * fcvt (double VALUE, int NDIGIT, int *DECPT, int
          *NEG)
     The function `fcvt' is like `ecvt', but NDIGIT specifies the
     number of digits after the decimal point.  If NDIGIT is less than
     zero, VALUE is rounded to the NDIGIT+1'th place to the left of the
     decimal point.  For example, if NDIGIT is `-1', VALUE will be
     rounded to the nearest 10.  If NDIGIT is negative and larger than
     the number of digits to the left of the decimal point in VALUE,
     VALUE will be rounded to one significant digit.

     If NDIGIT decimal digits would exceed the precision of a `double'
     it is reduced to a system-specific value.

     The returned string is statically allocated and overwritten by
     each call to `fcvt'.

 -- Function: char * gcvt (double VALUE, int NDIGIT, char *BUF)
     `gcvt' is functionally equivalent to `sprintf(buf, "%*g", ndigit,
     value'.  It is provided only for compatibility's sake.  It returns
     BUF.

     If NDIGIT decimal digits would exceed the precision of a `double'
     it is reduced to a system-specific value.

   As extensions, the GNU C library provides versions of these three
functions that take `long double' arguments.

 -- Function: char * qecvt (long double VALUE, int NDIGIT, int *DECPT,
          int *NEG)
     This function is equivalent to `ecvt' except that it takes a `long
     double' for the first parameter and that NDIGIT is restricted by
     the precision of a `long double'.

 -- Function: char * qfcvt (long double VALUE, int NDIGIT, int *DECPT,
          int *NEG)
     This function is equivalent to `fcvt' except that it takes a `long
     double' for the first parameter and that NDIGIT is restricted by
     the precision of a `long double'.

 -- Function: char * qgcvt (long double VALUE, int NDIGIT, char *BUF)
     This function is equivalent to `gcvt' except that it takes a `long
     double' for the first parameter and that NDIGIT is restricted by
     the precision of a `long double'.

   The `ecvt' and `fcvt' functions, and their `long double'
equivalents, all return a string located in a static buffer which is
overwritten by the next call to the function.  The GNU C library
provides another set of extended functions which write the converted
string into a user-supplied buffer.  These have the conventional `_r'
suffix.

   `gcvt_r' is not necessary, because `gcvt' already uses a
user-supplied buffer.

 -- Function: int ecvt_r (double VALUE, int NDIGIT, int *DECPT, int
          *NEG, char *BUF, size_t LEN)
     The `ecvt_r' function is the same as `ecvt', except that it places
     its result into the user-specified buffer pointed to by BUF, with
     length LEN.  The return value is `-1' in case of an error and zero
     otherwise.

     This function is a GNU extension.

 -- Function: int fcvt_r (double VALUE, int NDIGIT, int *DECPT, int
          *NEG, char *BUF, size_t LEN)
     The `fcvt_r' function is the same as `fcvt', except that it places
     its result into the user-specified buffer pointed to by BUF, with
     length LEN.  The return value is `-1' in case of an error and zero
     otherwise.

     This function is a GNU extension.

 -- Function: int qecvt_r (long double VALUE, int NDIGIT, int *DECPT,
          int *NEG, char *BUF, size_t LEN)
     The `qecvt_r' function is the same as `qecvt', except that it
     places its result into the user-specified buffer pointed to by
     BUF, with length LEN.  The return value is `-1' in case of an
     error and zero otherwise.

     This function is a GNU extension.

 -- Function: int qfcvt_r (long double VALUE, int NDIGIT, int *DECPT,
          int *NEG, char *BUF, size_t LEN)
     The `qfcvt_r' function is the same as `qfcvt', except that it
     places its result into the user-specified buffer pointed to by
     BUF, with length LEN.  The return value is `-1' in case of an
     error and zero otherwise.

     This function is a GNU extension.


File: libc.info,  Node: Date and Time,  Next: Resource Usage And Limitation,  Prev: Arithmetic,  Up: Top

21 Date and Time
****************

This chapter describes functions for manipulating dates and times,
including functions for determining what time it is and conversion
between different time representations.

* Menu:

* Time Basics::                 Concepts and definitions.
* Elapsed Time::                Data types to represent elapsed times
* Processor And CPU Time::      Time a program has spent executing.
* Calendar Time::               Manipulation of ``real'' dates and times.
* Setting an Alarm::            Sending a signal after a specified time.
* Sleeping::                    Waiting for a period of time.


File: libc.info,  Node: Time Basics,  Next: Elapsed Time,  Up: Date and Time

21.1 Time Basics
================

Discussing time in a technical manual can be difficult because the word
"time" in English refers to lots of different things.  In this manual,
we use a rigorous terminology to avoid confusion, and the only thing we
use the simple word "time" for is to talk about the abstract concept.

   A "calendar time" is a point in the time continuum, for example
November 4, 1990 at 18:02.5 UTC.  Sometimes this is called "absolute
time".  

   We don't speak of a "date", because that is inherent in a calendar
time.  

   An "interval" is a contiguous part of the time continuum between two
calendar times, for example the hour between 9:00 and 10:00 on July 4,
1980.  

   An "elapsed time" is the length of an interval, for example, 35
minutes.  People sometimes sloppily use the word "interval" to refer to
the elapsed time of some interval.  

   An "amount of time" is a sum of elapsed times, which need not be of
any specific intervals.  For example, the amount of time it takes to
read a book might be 9 hours, independently of when and in how many
sittings it is read.

   A "period" is the elapsed time of an interval between two events,
especially when they are part of a sequence of regularly repeating
events.  

   "CPU time" is like calendar time, except that it is based on the
subset of the time continuum when a particular process is actively
using a CPU.  CPU time is, therefore, relative to a process.  

   "Processor time" is an amount of time that a CPU is in use.  In
fact, it's a basic system resource, since there's a limit to how much
can exist in any given interval (that limit is the elapsed time of the
interval times the number of CPUs in the processor).  People often call
this CPU time, but we reserve the latter term in this manual for the
definition above.  


File: libc.info,  Node: Elapsed Time,  Next: Processor And CPU Time,  Prev: Time Basics,  Up: Date and Time

21.2 Elapsed Time
=================

One way to represent an elapsed time is with a simple arithmetic data
type, as with the following function to compute the elapsed time between
two calendar times.  This function is declared in `time.h'.

 -- Function: double difftime (time_t TIME1, time_t TIME0)
     The `difftime' function returns the number of seconds of elapsed
     time between calendar time TIME1 and calendar time TIME0, as a
     value of type `double'.  The difference ignores leap seconds
     unless leap second support is enabled.

     In the GNU system, you can simply subtract `time_t' values.  But on
     other systems, the `time_t' data type might use some other encoding
     where subtraction doesn't work directly.

   The GNU C library provides two data types specifically for
representing an elapsed time.  They are used by various GNU C library
functions, and you can use them for your own purposes too.  They're
exactly the same except that one has a resolution in microseconds, and
the other, newer one, is in nanoseconds.

 -- Data Type: struct timeval
     The `struct timeval' structure represents an elapsed time.  It is
     declared in `sys/time.h' and has the following members:

    `long int tv_sec'
          This represents the number of whole seconds of elapsed time.

    `long int tv_usec'
          This is the rest of the elapsed time (a fraction of a second),
          represented as the number of microseconds.  It is always less
          than one million.


 -- Data Type: struct timespec
     The `struct timespec' structure represents an elapsed time.  It is
     declared in `time.h' and has the following members:

    `long int tv_sec'
          This represents the number of whole seconds of elapsed time.

    `long int tv_nsec'
          This is the rest of the elapsed time (a fraction of a second),
          represented as the number of nanoseconds.  It is always less
          than one billion.


   It is often necessary to subtract two values of type
`struct timeval' or `struct timespec'.  Here is the best way to do
this.  It works even on some peculiar operating systems where the
`tv_sec' member has an unsigned type.

     /* Subtract the `struct timeval' values X and Y,
        storing the result in RESULT.
        Return 1 if the difference is negative, otherwise 0.  */

     int
     timeval_subtract (result, x, y)
          struct timeval *result, *x, *y;
     {
       /* Perform the carry for the later subtraction by updating Y. */
       if (x->tv_usec < y->tv_usec) {
         int nsec = (y->tv_usec - x->tv_usec) / 1000000 + 1;
         y->tv_usec -= 1000000 * nsec;
         y->tv_sec += nsec;
       }
       if (x->tv_usec - y->tv_usec > 1000000) {
         int nsec = (x->tv_usec - y->tv_usec) / 1000000;
         y->tv_usec += 1000000 * nsec;
         y->tv_sec -= nsec;
       }

       /* Compute the time remaining to wait.
          `tv_usec' is certainly positive. */
       result->tv_sec = x->tv_sec - y->tv_sec;
       result->tv_usec = x->tv_usec - y->tv_usec;

       /* Return 1 if result is negative. */
       return x->tv_sec < y->tv_sec;
     }

   Common functions that use `struct timeval' are `gettimeofday' and
`settimeofday'.

   There are no GNU C library functions specifically oriented toward
dealing with elapsed times, but the calendar time, processor time, and
alarm and sleeping functions have a lot to do with them.


File: libc.info,  Node: Processor And CPU Time,  Next: Calendar Time,  Prev: Elapsed Time,  Up: Date and Time

21.3 Processor And CPU Time
===========================

If you're trying to optimize your program or measure its efficiency,
it's very useful to know how much processor time it uses.  For that,
calendar time and elapsed times are useless because a process may spend
time waiting for I/O or for other processes to use the CPU.  However,
you can get the information with the functions in this section.

   CPU time (*note Time Basics::) is represented by the data type
`clock_t', which is a number of "clock ticks".  It gives the total
amount of time a process has actively used a CPU since some arbitrary
event.  On the GNU system, that event is the creation of the process.
While arbitrary in general, the event is always the same event for any
particular process, so you can always measure how much time on the CPU
a particular computation takes by examinining the process' CPU time
before and after the computation.  

   In the GNU system, `clock_t' is equivalent to `long int' and
`CLOCKS_PER_SEC' is an integer value.  But in other systems, both
`clock_t' and the macro `CLOCKS_PER_SEC' can be either integer or
floating-point types.  Casting CPU time values to `double', as in the
example above, makes sure that operations such as arithmetic and
printing work properly and consistently no matter what the underlying
representation is.

   Note that the clock can wrap around.  On a 32bit system with
`CLOCKS_PER_SEC' set to one million this function will return the same
value approximately every 72 minutes.

   For additional functions to examine a process' use of processor time,
and to control it, *Note Resource Usage And Limitation::.

* Menu:

* CPU Time::                    The `clock' function.
* Processor Time::              The `times' function.


File: libc.info,  Node: CPU Time,  Next: Processor Time,  Up: Processor And CPU Time

21.3.1 CPU Time Inquiry
-----------------------

To get a process' CPU time, you can use the `clock' function.  This
facility is declared in the header file `time.h'.  

   In typical usage, you call the `clock' function at the beginning and
end of the interval you want to time, subtract the values, and then
divide by `CLOCKS_PER_SEC' (the number of clock ticks per second) to
get processor time, like this:

     #include <time.h>

     clock_t start, end;
     double cpu_time_used;

     start = clock();
     ... /* Do the work. */
     end = clock();
     cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;

   Do not use a single CPU time as an amount of time; it doesn't work
that way.  Either do a subtraction as shown above or query processor
time directly.  *Note Processor Time::.

   Different computers and operating systems vary wildly in how they
keep track of CPU time.  It's common for the internal processor clock
to have a resolution somewhere between a hundredth and millionth of a
second.

 -- Macro: int CLOCKS_PER_SEC
     The value of this macro is the number of clock ticks per second
     measured by the `clock' function.  POSIX requires that this value
     be one million independent of the actual resolution.

 -- Macro: int CLK_TCK
     This is an obsolete name for `CLOCKS_PER_SEC'.

 -- Data Type: clock_t
     This is the type of the value returned by the `clock' function.
     Values of type `clock_t' are numbers of clock ticks.

 -- Function: clock_t clock (void)
     This function returns the calling process' current CPU time.  If
     the CPU time is not available or cannot be represented, `clock'
     returns the value `(clock_t)(-1)'.


File: libc.info,  Node: Processor Time,  Prev: CPU Time,  Up: Processor And CPU Time

21.3.2 Processor Time Inquiry
-----------------------------

The `times' function returns information about a process' consumption
of processor time in a `struct tms' object, in addition to the process'
CPU time.  *Note Time Basics::.  You should include the header file
`sys/times.h' to use this facility.  

 -- Data Type: struct tms
     The `tms' structure is used to return information about process
     times.  It contains at least the following members:

    `clock_t tms_utime'
          This is the total processor time the calling process has used
          in executing the instructions of its program.

    `clock_t tms_stime'
          This is the processor time the system has used on behalf of
          the calling process.

    `clock_t tms_cutime'
          This is the sum of the `tms_utime' values and the `tms_cutime'
          values of all terminated child processes of the calling
          process, whose status has been reported to the parent process
          by `wait' or `waitpid'; see *Note Process Completion::.  In
          other words, it represents the total processor time used in
          executing the instructions of all the terminated child
          processes of the calling process, excluding child processes
          which have not yet been reported by `wait' or `waitpid'.  

    `clock_t tms_cstime'
          This is similar to `tms_cutime', but represents the total
          processor time system has used on behalf of all the
          terminated child processes of the calling process.

     All of the times are given in numbers of clock ticks.  Unlike CPU
     time, these are the actual amounts of time; not relative to any
     event.  *Note Creating a Process::.

 -- Function: clock_t times (struct tms *BUFFER)
     The `times' function stores the processor time information for the
     calling process in BUFFER.

     The return value is the calling process' CPU time (the same value
     you get from `clock()'.  `times' returns `(clock_t)(-1)' to
     indicate failure.

   *Portability Note:* The `clock' function described in *Note CPU
Time:: is specified by the ISO C standard.  The `times' function is a
feature of POSIX.1.  In the GNU system, the CPU time is defined to be
equivalent to the sum of the `tms_utime' and `tms_stime' fields
returned by `times'.


File: libc.info,  Node: Calendar Time,  Next: Setting an Alarm,  Prev: Processor And CPU Time,  Up: Date and Time

21.4 Calendar Time
==================

This section describes facilities for keeping track of calendar time.
*Note Time Basics::.

   The GNU C library represents calendar time three ways:

   * "Simple time" (the `time_t' data type) is a compact
     representation, typically giving the number of seconds of elapsed
     time since some implementation-specific base time.  

   * There is also a "high-resolution time" representation.  Like simple
     time, this represents a calendar time as an elapsed time since a
     base time, but instead of measuring in whole seconds, it uses a
     `struct timeval' data type, which includes fractions of a second.
     Use this time representation instead of simple time when you need
     greater precision.  

   * "Local time" or "broken-down time" (the `struct tm' data type)
     represents a calendar time as a set of components specifying the
     year, month, and so on in the Gregorian calendar, for a specific
     time zone.  This calendar time representation is usually used only
     to communicate with people.  

* Menu:

* Simple Calendar Time::        Facilities for manipulating calendar time.
* High-Resolution Calendar::    A time representation with greater precision.
* Broken-down Time::            Facilities for manipulating local time.
* High Accuracy Clock::         Maintaining a high accuracy system clock.
* Formatting Calendar Time::    Converting times to strings.
* Parsing Date and Time::       Convert textual time and date information back
                                 into broken-down time values.
* TZ Variable::                 How users specify the time zone.
* Time Zone Functions::         Functions to examine or specify the time zone.
* Time Functions Example::      An example program showing use of some of
				 the time functions.


File: libc.info,  Node: Simple Calendar Time,  Next: High-Resolution Calendar,  Up: Calendar Time

21.4.1 Simple Calendar Time
---------------------------

This section describes the `time_t' data type for representing calendar
time as simple time, and the functions which operate on simple time
objects.  These facilities are declared in the header file `time.h'.  

 -- Data Type: time_t
     This is the data type used to represent simple time.  Sometimes,
     it also represents an elapsed time.  When interpreted as a
     calendar time value, it represents the number of seconds elapsed
     since 00:00:00 on January 1, 1970, Coordinated Universal Time.
     (This calendar time is sometimes referred to as the "epoch".)
     POSIX requires that this count not include leap seconds, but on
     some systems this count includes leap seconds if you set `TZ' to
     certain values (*note TZ Variable::).

     Note that a simple time has no concept of local time zone.
     Calendar Time T is the same instant in time regardless of where on
     the globe the computer is.

     In the GNU C library, `time_t' is equivalent to `long int'.  In
     other systems, `time_t' might be either an integer or
     floating-point type.

   The function `difftime' tells you the elapsed time between two
simple calendar times, which is not always as easy to compute as just
subtracting.  *Note Elapsed Time::.

 -- Function: time_t time (time_t *RESULT)
     The `time' function returns the current calendar time as a value of
     type `time_t'.  If the argument RESULT is not a null pointer, the
     calendar time value is also stored in `*RESULT'.  If the current
     calendar time is not available, the value `(time_t)(-1)' is
     returned.

 -- Function: int stime (time_t *NEWTIME)
     `stime' sets the system clock, i.e.  it tells the system that the
     current calendar time is NEWTIME, where `newtime' is interpreted
     as described in the above definition of `time_t'.

     `settimeofday' is a newer function which sets the system clock to
     better than one second precision.  `settimeofday' is generally a
     better choice than `stime'.  *Note High-Resolution Calendar::.

     Only the superuser can set the system clock.

     If the function succeeds, the return value is zero.  Otherwise, it
     is `-1' and `errno' is set accordingly:

    `EPERM'
          The process is not superuser.


File: libc.info,  Node: High-Resolution Calendar,  Next: Broken-down Time,  Prev: Simple Calendar Time,  Up: Calendar Time

21.4.2 High-Resolution Calendar
-------------------------------

The `time_t' data type used to represent simple times has a resolution
of only one second.  Some applications need more precision.

   So, the GNU C library also contains functions which are capable of
representing calendar times to a higher resolution than one second.  The
functions and the associated data types described in this section are
declared in `sys/time.h'.  

 -- Data Type: struct timezone
     The `struct timezone' structure is used to hold minimal information
     about the local time zone.  It has the following members:

    `int tz_minuteswest'
          This is the number of minutes west of UTC.

    `int tz_dsttime'
          If nonzero, Daylight Saving Time applies during some part of
          the year.

     The `struct timezone' type is obsolete and should never be used.
     Instead, use the facilities described in *Note Time Zone
     Functions::.

 -- Function: int gettimeofday (struct timeval *TP, struct timezone
          *TZP)
     The `gettimeofday' function returns the current calendar time as
     the elapsed time since the epoch in the `struct timeval' structure
     indicated by TP.  (*note Elapsed Time:: for a description of
     `struct timeval').  Information about the time zone is returned in
     the structure pointed at TZP.  If the TZP argument is a null
     pointer, time zone information is ignored.

     The return value is `0' on success and `-1' on failure.  The
     following `errno' error condition is defined for this function:

    `ENOSYS'
          The operating system does not support getting time zone
          information, and TZP is not a null pointer.  The GNU
          operating system does not support using `struct timezone' to
          represent time zone information; that is an obsolete feature
          of 4.3 BSD.  Instead, use the facilities described in *Note
          Time Zone Functions::.

 -- Function: int settimeofday (const struct timeval *TP, const struct
          timezone *TZP)
     The `settimeofday' function sets the current calendar time in the
     system clock according to the arguments.  As for `gettimeofday',
     the calendar time is represented as the elapsed time since the
     epoch.  As for `gettimeofday', time zone information is ignored if
     TZP is a null pointer.

     You must be a privileged user in order to use `settimeofday'.

     Some kernels automatically set the system clock from some source
     such as a hardware clock when they start up.  Others, including
     Linux, place the system clock in an "invalid" state (in which
     attempts to read the clock fail).  A call of `stime' removes the
     system clock from an invalid state, and system startup scripts
     typically run a program that calls `stime'.

     `settimeofday' causes a sudden jump forwards or backwards, which
     can cause a variety of problems in a system.  Use `adjtime' (below)
     to make a smooth transition from one time to another by temporarily
     speeding up or slowing down the clock.

     With a Linux kernel, `adjtimex' does the same thing and can also
     make permanent changes to the speed of the system clock so it
     doesn't need to be corrected as often.

     The return value is `0' on success and `-1' on failure.  The
     following `errno' error conditions are defined for this function:

    `EPERM'
          This process cannot set the clock because it is not
          privileged.

    `ENOSYS'
          The operating system does not support setting time zone
          information, and TZP is not a null pointer.

 -- Function: int adjtime (const struct timeval *DELTA, struct timeval
          *OLDDELTA)
     This function speeds up or slows down the system clock in order to
     make a gradual adjustment.  This ensures that the calendar time
     reported by the system clock is always monotonically increasing,
     which might not happen if you simply set the clock.

     The DELTA argument specifies a relative adjustment to be made to
     the clock time.  If negative, the system clock is slowed down for a
     while until it has lost this much elapsed time.  If positive, the
     system clock is speeded up for a while.

     If the OLDDELTA argument is not a null pointer, the `adjtime'
     function returns information about any previous time adjustment
     that has not yet completed.

     This function is typically used to synchronize the clocks of
     computers in a local network.  You must be a privileged user to
     use it.

     With a Linux kernel, you can use the `adjtimex' function to
     permanently change the clock speed.

     The return value is `0' on success and `-1' on failure.  The
     following `errno' error condition is defined for this function:

    `EPERM'
          You do not have privilege to set the time.

   *Portability Note:*  The `gettimeofday', `settimeofday', and
`adjtime' functions are derived from BSD.

   Symbols for the following function are declared in `sys/timex.h'.

 -- Function: int adjtimex (struct timex *TIMEX)
     `adjtimex' is functionally identical to `ntp_adjtime'.  *Note High
     Accuracy Clock::.

     This function is present only with a Linux kernel.



File: libc.info,  Node: Broken-down Time,  Next: High Accuracy Clock,  Prev: High-Resolution Calendar,  Up: Calendar Time

21.4.3 Broken-down Time
-----------------------

Calendar time is represented by the usual GNU C library functions as an
elapsed time since a fixed base calendar time.  This is convenient for
computation, but has no relation to the way people normally think of
calendar time.  By contrast, "broken-down time" is a binary
representation of calendar time separated into year, month, day, and so
on.  Broken-down time values are not useful for calculations, but they
are useful for printing human readable time information.

   A broken-down time value is always relative to a choice of time
zone, and it also indicates which time zone that is.

   The symbols in this section are declared in the header file `time.h'.

 -- Data Type: struct tm
     This is the data type used to represent a broken-down time.  The
     structure contains at least the following members, which can
     appear in any order.

    `int tm_sec'
          This is the number of full seconds since the top of the
          minute (normally in the range `0' through `59', but the
          actual upper limit is `60', to allow for leap seconds if leap
          second support is available).  

    `int tm_min'
          This is the number of full minutes since the top of the hour
          (in the range `0' through `59').

    `int tm_hour'
          This is the number of full hours past midnight (in the range
          `0' through `23').

    `int tm_mday'
          This is the ordinal day of the month (in the range `1'
          through `31').  Watch out for this one!  As the only ordinal
          number in the structure, it is inconsistent with the rest of
          the structure.

    `int tm_mon'
          This is the number of full calendar months since the
          beginning of the year (in the range `0' through `11').  Watch
          out for this one!  People usually use ordinal numbers for
          month-of-year (where January = 1).

    `int tm_year'
          This is the number of full calendar years since 1900.

    `int tm_wday'
          This is the number of full days since Sunday (in the range
          `0' through `6').

    `int tm_yday'
          This is the number of full days since the beginning of the
          year (in the range `0' through `365').

    `int tm_isdst'
          This is a flag that indicates whether Daylight Saving Time is
          (or was, or will be) in effect at the time described.  The
          value is positive if Daylight Saving Time is in effect, zero
          if it is not, and negative if the information is not
          available.

    `long int tm_gmtoff'
          This field describes the time zone that was used to compute
          this broken-down time value, including any adjustment for
          daylight saving; it is the number of seconds that you must
          add to UTC to get local time.  You can also think of this as
          the number of seconds east of UTC.  For example, for U.S.
          Eastern Standard Time, the value is `-5*60*60'.  The
          `tm_gmtoff' field is derived from BSD and is a GNU library
          extension; it is not visible in a strict ISO C environment.

    `const char *tm_zone'
          This field is the name for the time zone that was used to
          compute this broken-down time value.  Like `tm_gmtoff', this
          field is a BSD and GNU extension, and is not visible in a
          strict ISO C environment.

 -- Function: struct tm * localtime (const time_t *TIME)
     The `localtime' function converts the simple time pointed to by
     TIME to broken-down time representation, expressed relative to the
     user's specified time zone.

     The return value is a pointer to a static broken-down time
     structure, which might be overwritten by subsequent calls to
     `ctime', `gmtime', or `localtime'.  (But no other library function
     overwrites the contents of this object.)

     The return value is the null pointer if TIME cannot be represented
     as a broken-down time; typically this is because the year cannot
     fit into an `int'.

     Calling `localtime' has one other effect: it sets the variable
     `tzname' with information about the current time zone.  *Note Time
     Zone Functions::.

   Using the `localtime' function is a big problem in multi-threaded
programs.  The result is returned in a static buffer and this is used in
all threads.  POSIX.1c introduced a variant of this function.

 -- Function: struct tm * localtime_r (const time_t *TIME, struct tm
          *RESULTP)
     The `localtime_r' function works just like the `localtime'
     function.  It takes a pointer to a variable containing a simple
     time and converts it to the broken-down time format.

     But the result is not placed in a static buffer.  Instead it is
     placed in the object of type `struct tm' to which the parameter
     RESULTP points.

     If the conversion is successful the function returns a pointer to
     the object the result was written into, i.e., it returns RESULTP.

 -- Function: struct tm * gmtime (const time_t *TIME)
     This function is similar to `localtime', except that the
     broken-down time is expressed as Coordinated Universal Time (UTC)
     (formerly called Greenwich Mean Time (GMT)) rather than relative
     to a local time zone.


   As for the `localtime' function we have the problem that the result
is placed in a static variable.  POSIX.1c also provides a replacement
for `gmtime'.

 -- Function: struct tm * gmtime_r (const time_t *TIME, struct tm
          *RESULTP)
     This function is similar to `localtime_r', except that it converts
     just like `gmtime' the given time as Coordinated Universal Time.

     If the conversion is successful the function returns a pointer to
     the object the result was written into, i.e., it returns RESULTP.

 -- Function: time_t mktime (struct tm *BROKENTIME)
     The `mktime' function is used to convert a broken-down time
     structure to a simple time representation.  It also "normalizes"
     the contents of the broken-down time structure, by filling in the
     day of week and day of year based on the other date and time
     components.

     The `mktime' function ignores the specified contents of the
     `tm_wday' and `tm_yday' members of the broken-down time structure.
     It uses the values of the other components to determine the
     calendar time; it's permissible for these components to have
     unnormalized values outside their normal ranges.  The last thing
     that `mktime' does is adjust the components of the BROKENTIME
     structure (including the `tm_wday' and `tm_yday').

     If the specified broken-down time cannot be represented as a
     simple time, `mktime' returns a value of `(time_t)(-1)' and does
     not modify the contents of BROKENTIME.

     Calling `mktime' also sets the variable `tzname' with information
     about the current time zone.  *Note Time Zone Functions::.

 -- Function: time_t timelocal (struct tm *BROKENTIME)
     `timelocal' is functionally identical to `mktime', but more
     mnemonically named.  Note that it is the inverse of the `localtime'
     function.

     *Portability note:*  `mktime' is essentially universally
     available.  `timelocal' is rather rare.


 -- Function: time_t timegm (struct tm *BROKENTIME)
     `timegm' is functionally identical to `mktime' except it always
     takes the input values to be Coordinated Universal Time (UTC)
     regardless of any local time zone setting.

     Note that `timegm' is the inverse of `gmtime'.

     *Portability note:*  `mktime' is essentially universally
     available.  `timegm' is rather rare.  For the most portable
     conversion from a UTC broken-down time to a simple time, set the
     `TZ' environment variable to UTC, call `mktime', then set `TZ'
     back.



File: libc.info,  Node: High Accuracy Clock,  Next: Formatting Calendar Time,  Prev: Broken-down Time,  Up: Calendar Time

21.4.4 High Accuracy Clock
--------------------------

The `ntp_gettime' and `ntp_adjtime' functions provide an interface to
monitor and manipulate the system clock to maintain high accuracy time.
For example, you can fine tune the speed of the clock or synchronize
it with another time source.

   A typical use of these functions is by a server implementing the
Network Time Protocol to synchronize the clocks of multiple systems and
high precision clocks.

   These functions are declared in `sys/timex.h'.

 -- Data Type: struct ntptimeval
     This structure is used for information about the system clock.  It
     contains the following members:
    `struct timeval time'
          This is the current calendar time, expressed as the elapsed
          time since the epoch.  The `struct timeval' data type is
          described in *Note Elapsed Time::.

    `long int maxerror'
          This is the maximum error, measured in microseconds.  Unless
          updated via `ntp_adjtime' periodically, this value will reach
          some platform-specific maximum value.

    `long int esterror'
          This is the estimated error, measured in microseconds.  This
          value can be set by `ntp_adjtime' to indicate the estimated
          offset of the system clock from the true calendar time.

 -- Function: int ntp_gettime (struct ntptimeval *TPTR)
     The `ntp_gettime' function sets the structure pointed to by TPTR
     to current values.  The elements of the structure afterwards
     contain the values the timer implementation in the kernel assumes.
     They might or might not be correct.  If they are not a
     `ntp_adjtime' call is necessary.

     The return value is `0' on success and other values on failure.
     The following `errno' error conditions are defined for this
     function:

    `TIME_ERROR'
          The precision clock model is not properly set up at the
          moment, thus the clock must be considered unsynchronized, and
          the values should be treated with care.

 -- Data Type: struct timex
     This structure is used to control and monitor the system clock.  It
     contains the following members:
    `unsigned int modes'
          This variable controls whether and which values are set.
          Several symbolic constants have to be combined with _binary
          or_ to specify the effective mode.  These constants start
          with `MOD_'.

    `long int offset'
          This value indicates the current offset of the system clock
          from the true calendar time.  The value is given in
          microseconds.  If bit `MOD_OFFSET' is set in `modes', the
          offset (and possibly other dependent values) can be set.  The
          offset's absolute value must not exceed `MAXPHASE'.

    `long int frequency'
          This value indicates the difference in frequency between the
          true calendar time and the system clock.  The value is
          expressed as scaled PPM (parts per million, 0.0001%).  The
          scaling is `1 << SHIFT_USEC'.  The value can be set with bit
          `MOD_FREQUENCY', but the absolute value must not exceed
          `MAXFREQ'.

    `long int maxerror'
          This is the maximum error, measured in microseconds.  A new
          value can be set using bit `MOD_MAXERROR'.  Unless updated via
          `ntp_adjtime' periodically, this value will increase steadily
          and reach some platform-specific maximum value.

    `long int esterror'
          This is the estimated error, measured in microseconds.  This
          value can be set using bit `MOD_ESTERROR'.

    `int status'
          This variable reflects the various states of the clock
          machinery.  There are symbolic constants for the significant
          bits, starting with `STA_'.  Some of these flags can be
          updated using the `MOD_STATUS' bit.

    `long int constant'
          This value represents the bandwidth or stiffness of the PLL
          (phase locked loop) implemented in the kernel.  The value can
          be changed using bit `MOD_TIMECONST'.

    `long int precision'
          This value represents the accuracy or the maximum error when
          reading the system clock.  The value is expressed in
          microseconds.

    `long int tolerance'
          This value represents the maximum frequency error of the
          system clock in scaled PPM.  This value is used to increase
          the `maxerror' every second.

    `struct timeval time'
          The current calendar time.

    `long int tick'
          The elapsed time between clock ticks in microseconds.  A
          clock tick is a periodic timer interrupt on which the system
          clock is based.

    `long int ppsfreq'
          This is the first of a few optional variables that are
          present only if the system clock can use a PPS (pulse per
          second) signal to discipline the system clock.  The value is
          expressed in scaled PPM and it denotes the difference in
          frequency between the system clock and the PPS signal.

    `long int jitter'
          This value expresses a median filtered average of the PPS
          signal's dispersion in microseconds.

    `int shift'
          This value is a binary exponent for the duration of the PPS
          calibration interval, ranging from `PPS_SHIFT' to
          `PPS_SHIFTMAX'.

    `long int stabil'
          This value represents the median filtered dispersion of the
          PPS frequency in scaled PPM.

    `long int jitcnt'
          This counter represents the number of pulses where the jitter
          exceeded the allowed maximum `MAXTIME'.

    `long int calcnt'
          This counter reflects the number of successful calibration
          intervals.

    `long int errcnt'
          This counter represents the number of calibration errors
          (caused by large offsets or jitter).

    `long int stbcnt'
          This counter denotes the number of of calibrations where the
          stability exceeded the threshold.

 -- Function: int ntp_adjtime (struct timex *TPTR)
     The `ntp_adjtime' function sets the structure specified by TPTR to
     current values.

     In addition, `ntp_adjtime' updates some settings to match what you
     pass to it in *TPTR.  Use the `modes' element of *TPTR to select
     what settings to update.  You can set `offset', `freq',
     `maxerror', `esterror', `status', `constant', and `tick'.

     `modes' = zero means set nothing.

     Only the superuser can update settings.

     The return value is `0' on success and other values on failure.
     The following `errno' error conditions are defined for this
     function:

    `TIME_ERROR'
          The high accuracy clock model is not properly set up at the
          moment, thus the clock must be considered unsynchronized, and
          the values should be treated with care.  Another reason could
          be that the specified new values are not allowed.

    `EPERM'
          The process specified a settings update, but is not superuser.


     For more details see RFC1305 (Network Time Protocol, Version 3) and
     related documents.

     *Portability note:* Early versions of the GNU C library did not
     have this function but did have the synonymous `adjtimex'.



File: libc.info,  Node: Formatting Calendar Time,  Next: Parsing Date and Time,  Prev: High Accuracy Clock,  Up: Calendar Time

21.4.5 Formatting Calendar Time
-------------------------------

The functions described in this section format calendar time values as
strings.  These functions are declared in the header file `time.h'.  

 -- Function: char * asctime (const struct tm *BROKENTIME)
     The `asctime' function converts the broken-down time value that
     BROKENTIME points to into a string in a standard format:

          "Tue May 21 13:46:22 1991\n"

     The abbreviations for the days of week are: `Sun', `Mon', `Tue',
     `Wed', `Thu', `Fri', and `Sat'.

     The abbreviations for the months are: `Jan', `Feb', `Mar', `Apr',
     `May', `Jun', `Jul', `Aug', `Sep', `Oct', `Nov', and `Dec'.

     The return value points to a statically allocated string, which
     might be overwritten by subsequent calls to `asctime' or `ctime'.
     (But no other library function overwrites the contents of this
     string.)

 -- Function: char * asctime_r (const struct tm *BROKENTIME, char
          *BUFFER)
     This function is similar to `asctime' but instead of placing the
     result in a static buffer it writes the string in the buffer
     pointed to by the parameter BUFFER.  This buffer should have room
     for at least 26 bytes, including the terminating null.

     If no error occurred the function returns a pointer to the string
     the result was written into, i.e., it returns BUFFER.  Otherwise
     return `NULL'.

 -- Function: char * ctime (const time_t *TIME)
     The `ctime' function is similar to `asctime', except that you
     specify the calendar time argument as a `time_t' simple time value
     rather than in broken-down local time format.  It is equivalent to

          asctime (localtime (TIME))

     `ctime' sets the variable `tzname', because `localtime' does so.
     *Note Time Zone Functions::.

 -- Function: char * ctime_r (const time_t *TIME, char *BUFFER)
     This function is similar to `ctime', but places the result in the
     string pointed to by BUFFER.  It is equivalent to (written using
     gcc extensions, *note Statement Exprs: (gcc)Statement Exprs.):

          ({ struct tm tm; asctime_r (localtime_r (time, &tm), buf); })

     If no error occurred the function returns a pointer to the string
     the result was written into, i.e., it returns BUFFER.  Otherwise
     return `NULL'.

 -- Function: size_t strftime (char *S, size_t SIZE, const char
          *TEMPLATE, const struct tm *BROKENTIME)
     This function is similar to the `sprintf' function (*note
     Formatted Input::), but the conversion specifications that can
     appear in the format template TEMPLATE are specialized for
     printing components of the date and time BROKENTIME according to
     the locale currently specified for time conversion (*note
     Locales::).

     Ordinary characters appearing in the TEMPLATE are copied to the
     output string S; this can include multibyte character sequences.
     Conversion specifiers are introduced by a `%' character, followed
     by an optional flag which can be one of the following.  These flags
     are all GNU extensions. The first three affect only the output of
     numbers:

    `_'
          The number is padded with spaces.

    `-'
          The number is not padded at all.

    `0'
          The number is padded with zeros even if the format specifies
          padding with spaces.

    `^'
          The output uses uppercase characters, but only if this is
          possible (*note Case Conversion::).

     The default action is to pad the number with zeros to keep it a
     constant width.  Numbers that do not have a range indicated below
     are never padded, since there is no natural width for them.

     Following the flag an optional specification of the width is
     possible.  This is specified in decimal notation.  If the natural
     size of the output is of the field has less than the specified
     number of characters, the result is written right adjusted and
     space padded to the given size.

     An optional modifier can follow the optional flag and width
     specification.  The modifiers, which were first standardized by
     POSIX.2-1992 and by ISO C99, are:

    `E'
          Use the locale's alternate representation for date and time.
          This modifier applies to the `%c', `%C', `%x', `%X', `%y' and
          `%Y' format specifiers.  In a Japanese locale, for example,
          `%Ex' might yield a date format based on the Japanese
          Emperors' reigns.

    `O'
          Use the locale's alternate numeric symbols for numbers.  This
          modifier applies only to numeric format specifiers.

     If the format supports the modifier but no alternate representation
     is available, it is ignored.

     The conversion specifier ends with a format specifier taken from
     the following list.  The whole `%' sequence is replaced in the
     output string as follows:

    `%a'
          The abbreviated weekday name according to the current locale.

    `%A'
          The full weekday name according to the current locale.

    `%b'
          The abbreviated month name according to the current locale.

    `%B'
          The full month name according to the current locale.

    `%c'
          The preferred calendar time representation for the current
          locale.

    `%C'
          The century of the year.  This is equivalent to the greatest
          integer not greater than the year divided by 100.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%d'
          The day of the month as a decimal number (range `01' through
          `31').

    `%D'
          The date using the format `%m/%d/%y'.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%e'
          The day of the month like with `%d', but padded with blank
          (range ` 1' through `31').

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%F'
          The date using the format `%Y-%m-%d'.  This is the form
          specified in the ISO 8601 standard and is the preferred form
          for all uses.

          This format was first standardized by ISO C99 and by
          POSIX.1-2001.

    `%g'
          The year corresponding to the ISO week number, but without
          the century (range `00' through `99').  This has the same
          format and value as `%y', except that if the ISO week number
          (see `%V') belongs to the previous or next year, that year is
          used instead.

          This format was first standardized by ISO C99 and by
          POSIX.1-2001.

    `%G'
          The year corresponding to the ISO week number.  This has the
          same format and value as `%Y', except that if the ISO week
          number (see `%V') belongs to the previous or next year, that
          year is used instead.

          This format was first standardized by ISO C99 and by
          POSIX.1-2001 but was previously available as a GNU extension.

    `%h'
          The abbreviated month name according to the current locale.
          The action is the same as for `%b'.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%H'
          The hour as a decimal number, using a 24-hour clock (range
          `00' through `23').

    `%I'
          The hour as a decimal number, using a 12-hour clock (range
          `01' through `12').

    `%j'
          The day of the year as a decimal number (range `001' through
          `366').

    `%k'
          The hour as a decimal number, using a 24-hour clock like
          `%H', but padded with blank (range ` 0' through `23').

          This format is a GNU extension.

    `%l'
          The hour as a decimal number, using a 12-hour clock like
          `%I', but padded with blank (range ` 1' through `12').

          This format is a GNU extension.

    `%m'
          The month as a decimal number (range `01' through `12').

    `%M'
          The minute as a decimal number (range `00' through `59').

    `%n'
          A single `\n' (newline) character.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%p'
          Either `AM' or `PM', according to the given time value; or the
          corresponding strings for the current locale.  Noon is
          treated as `PM' and midnight as `AM'.  In most locales
          `AM'/`PM' format is not supported, in such cases `"%p"'
          yields an empty string.

    `%P'
          Either `am' or `pm', according to the given time value; or the
          corresponding strings for the current locale, printed in
          lowercase characters.  Noon is treated as `pm' and midnight
          as `am'.  In most locales `AM'/`PM' format is not supported,
          in such cases `"%P"' yields an empty string.

          This format is a GNU extension.

    `%r'
          The complete calendar time using the AM/PM format of the
          current locale.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.  In the POSIX locale, this format is equivalent to
          `%I:%M:%S %p'.

    `%R'
          The hour and minute in decimal numbers using the format
          `%H:%M'.

          This format was first standardized by ISO C99 and by
          POSIX.1-2001 but was previously available as a GNU extension.

    `%s'
          The number of seconds since the epoch, i.e., since 1970-01-01
          00:00:00 UTC.  Leap seconds are not counted unless leap
          second support is available.

          This format is a GNU extension.

    `%S'
          The seconds as a decimal number (range `00' through `60').

    `%t'
          A single `\t' (tabulator) character.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%T'
          The time of day using decimal numbers using the format
          `%H:%M:%S'.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%u'
          The day of the week as a decimal number (range `1' through
          `7'), Monday being `1'.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%U'
          The week number of the current year as a decimal number
          (range `00' through `53'), starting with the first Sunday as
          the first day of the first week.  Days preceding the first
          Sunday in the year are considered to be in week `00'.

    `%V'
          The ISO 8601:1988 week number as a decimal number (range `01'
          through `53').  ISO weeks start with Monday and end with
          Sunday.  Week `01' of a year is the first week which has the
          majority of its days in that year; this is equivalent to the
          week containing the year's first Thursday, and it is also
          equivalent to the week containing January 4.  Week `01' of a
          year can contain days from the previous year.  The week
          before week `01' of a year is the last week (`52' or `53') of
          the previous year even if it contains days from the new year.

          This format was first standardized by POSIX.2-1992 and by
          ISO C99.

    `%w'
          The day of the week as a decimal number (range `0' through
          `6'), Sunday being `0'.

    `%W'
          The week number of the current year as a decimal number
          (range `00' through `53'), starting with the first Monday as
          the first day of the first week.  All days preceding the
          first Monday in the year are considered to be in week `00'.

    `%x'
          The preferred date representation for the current locale.

    `%X'
          The preferred time of day representation for the current
          locale.

    `%y'
          The year without a century as a decimal number (range `00'
          through `99').  This is equivalent to the year modulo 100.

    `%Y'
          The year as a decimal number, using the Gregorian calendar.
          Years before the year `1' are numbered `0', `-1', and so on.

    `%z'
          RFC 822/ISO 8601:1988 style numeric time zone (e.g., `-0600'
          or `+0100'), or nothing if no time zone is determinable.

          This format was first standardized by ISO C99 and by
          POSIX.1-2001 but was previously available as a GNU extension.

          In the POSIX locale, a full RFC 822 timestamp is generated by
          the format `"%a, %d %b %Y %H:%M:%S %z"' (or the equivalent
          `"%a, %d %b %Y %T %z"').

    `%Z'
          The time zone abbreviation (empty if the time zone can't be
          determined).

    `%%'
          A literal `%' character.

     The SIZE parameter can be used to specify the maximum number of
     characters to be stored in the array S, including the terminating
     null character.  If the formatted time requires more than SIZE
     characters, `strftime' returns zero and the contents of the array
     S are undefined.  Otherwise the return value indicates the number
     of characters placed in the array S, not including the terminating
     null character.

     _Warning:_ This convention for the return value which is prescribed
     in ISO C can lead to problems in some situations.  For certain
     format strings and certain locales the output really can be the
     empty string and this cannot be discovered by testing the return
     value only.  E.g., in most locales the AM/PM time format is not
     supported (most of the world uses the 24 hour time
     representation).  In such locales `"%p"' will return the empty
     string, i.e., the return value is zero.  To detect situations like
     this something similar to the following code should be used:

          buf[0] = '\1';
          len = strftime (buf, bufsize, format, tp);
          if (len == 0 && buf[0] != '\0')
            {
              /* Something went wrong in the strftime call.  */
              ...
            }

     If S is a null pointer, `strftime' does not actually write
     anything, but instead returns the number of characters it would
     have written.

     According to POSIX.1 every call to `strftime' implies a call to
     `tzset'.  So the contents of the environment variable `TZ' is
     examined before any output is produced.

     For an example of `strftime', see *Note Time Functions Example::.

 -- Function: size_t wcsftime (wchar_t *S, size_t SIZE, const wchar_t
          *TEMPLATE, const struct tm *BROKENTIME)
     The `wcsftime' function is equivalent to the `strftime' function
     with the difference that it operates on wide character strings.
     The buffer where the result is stored, pointed to by S, must be an
     array of wide characters.  The parameter SIZE which specifies the
     size of the output buffer gives the number of wide character, not
     the number of bytes.

     Also the format string TEMPLATE is a wide character string.  Since
     all characters needed to specify the format string are in the basic
     character set it is portably possible to write format strings in
     the C source code using the `L"..."' notation.  The parameter
     BROKENTIME has the same meaning as in the `strftime' call.

     The `wcsftime' function supports the same flags, modifiers, and
     format specifiers as the `strftime' function.

     The return value of `wcsftime' is the number of wide characters
     stored in `s'.  When more characters would have to be written than
     can be placed in the buffer S the return value is zero, with the
     same problems indicated in the `strftime' documentation.


File: libc.info,  Node: Parsing Date and Time,  Next: TZ Variable,  Prev: Formatting Calendar Time,  Up: Calendar Time

21.4.6 Convert textual time and date information back
-----------------------------------------------------

The ISO C standard does not specify any functions which can convert the
output of the `strftime' function back into a binary format.  This led
to a variety of more-or-less successful implementations with different
interfaces over the years.  Then the Unix standard was extended by the
addition of two functions: `strptime' and `getdate'.  Both have strange
interfaces but at least they are widely available.

* Menu:

* Low-Level Time String Parsing::  Interpret string according to given format.
* General Time String Parsing::    User-friendly function to parse data and
                                    time strings.


File: libc.info,  Node: Low-Level Time String Parsing,  Next: General Time String Parsing,  Up: Parsing Date and Time

21.4.6.1 Interpret string according to given format
...................................................

he first function is rather low-level.  It is nevertheless frequently
used in software since it is better known.  Its interface and
implementation are heavily influenced by the `getdate' function, which
is defined and implemented in terms of calls to `strptime'.

 -- Function: char * strptime (const char *S, const char *FMT, struct
          tm *TP)
     The `strptime' function parses the input string S according to the
     format string FMT and stores its results in the structure TP.

     The input string could be generated by a `strftime' call or
     obtained any other way.  It does not need to be in a
     human-recognizable format; e.g. a date passed as `"02:1999:9"' is
     acceptable, even though it is ambiguous without context.  As long
     as the format string FMT matches the input string the function
     will succeed.

     The user has to make sure, though, that the input can be parsed in
     a unambiguous way.  The string `"1999112"' can be parsed using the
     format `"%Y%m%d"' as 1999-1-12, 1999-11-2, or even 19991-1-2.  It
     is necessary to add appropriate separators to reliably get results.

     The format string consists of the same components as the format
     string of the `strftime' function.  The only difference is that
     the flags `_', `-', `0', and `^' are not allowed.  Several of the
     distinct formats of `strftime' do the same work in `strptime'
     since differences like case of the input do not matter.  For
     reasons of symmetry all formats are supported, though.

     The modifiers `E' and `O' are also allowed everywhere the
     `strftime' function allows them.

     The formats are:

    `%a'
    `%A'
          The weekday name according to the current locale, in
          abbreviated form or the full name.

    `%b'
    `%B'
    `%h'
          The month name according to the current locale, in
          abbreviated form or the full name.

    `%c'
          The date and time representation for the current locale.

    `%Ec'
          Like `%c' but the locale's alternative date and time format
          is used.

    `%C'
          The century of the year.

          It makes sense to use this format only if the format string
          also contains the `%y' format.

    `%EC'
          The locale's representation of the period.

          Unlike `%C' it sometimes makes sense to use this format since
          some cultures represent years relative to the beginning of
          eras instead of using the Gregorian years.

    `%d'

    `%e'
          The day of the month as a decimal number (range `1' through
          `31').  Leading zeroes are permitted but not required.

    `%Od'
    `%Oe'
          Same as `%d' but using the locale's alternative numeric
          symbols.

          Leading zeroes are permitted but not required.

    `%D'
          Equivalent to `%m/%d/%y'.

    `%F'
          Equivalent to `%Y-%m-%d', which is the ISO 8601 date format.

          This is a GNU extension following an ISO C99 extension to
          `strftime'.

    `%g'
          The year corresponding to the ISO week number, but without
          the century (range `00' through `99').

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

          This format is a GNU extension following a GNU extension of
          `strftime'.

    `%G'
          The year corresponding to the ISO week number.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

          This format is a GNU extension following a GNU extension of
          `strftime'.

    `%H'
    `%k'
          The hour as a decimal number, using a 24-hour clock (range
          `00' through `23').

          `%k' is a GNU extension following a GNU extension of
          `strftime'.

    `%OH'
          Same as `%H' but using the locale's alternative numeric
          symbols.

    `%I'
    `%l'
          The hour as a decimal number, using a 12-hour clock (range
          `01' through `12').

          `%l' is a GNU extension following a GNU extension of
          `strftime'.

    `%OI'
          Same as `%I' but using the locale's alternative numeric
          symbols.

    `%j'
          The day of the year as a decimal number (range `1' through
          `366').

          Leading zeroes are permitted but not required.

    `%m'
          The month as a decimal number (range `1' through `12').

          Leading zeroes are permitted but not required.

    `%Om'
          Same as `%m' but using the locale's alternative numeric
          symbols.

    `%M'
          The minute as a decimal number (range `0' through `59').

          Leading zeroes are permitted but not required.

    `%OM'
          Same as `%M' but using the locale's alternative numeric
          symbols.

    `%n'
    `%t'
          Matches any white space.

    `%p'

    `%P'
          The locale-dependent equivalent to `AM' or `PM'.

          This format is not useful unless `%I' or `%l' is also used.
          Another complication is that the locale might not define
          these values at all and therefore the conversion fails.

          `%P' is a GNU extension following a GNU extension to
          `strftime'.

    `%r'
          The complete time using the AM/PM format of the current
          locale.

          A complication is that the locale might not define this
          format at all and therefore the conversion fails.

    `%R'
          The hour and minute in decimal numbers using the format
          `%H:%M'.

          `%R' is a GNU extension following a GNU extension to
          `strftime'.

    `%s'
          The number of seconds since the epoch, i.e., since 1970-01-01
          00:00:00 UTC.  Leap seconds are not counted unless leap
          second support is available.

          `%s' is a GNU extension following a GNU extension to
          `strftime'.

    `%S'
          The seconds as a decimal number (range `0' through `60').

          Leading zeroes are permitted but not required.

          *Note_* The Unix specification says the upper bound on this
          value is `61', a result of a decision to allow double leap
          seconds.  You will not see the value `61' because no minute
          has more than one leap second, but the myth persists.

    `%OS'
          Same as `%S' but using the locale's alternative numeric
          symbols.

    `%T'
          Equivalent to the use of `%H:%M:%S' in this place.

    `%u'
          The day of the week as a decimal number (range `1' through
          `7'), Monday being `1'.

          Leading zeroes are permitted but not required.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

    `%U'
          The week number of the current year as a decimal number
          (range `0' through `53').

          Leading zeroes are permitted but not required.

    `%OU'
          Same as `%U' but using the locale's alternative numeric
          symbols.

    `%V'
          The ISO 8601:1988 week number as a decimal number (range `1'
          through `53').

          Leading zeroes are permitted but not required.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

    `%w'
          The day of the week as a decimal number (range `0' through
          `6'), Sunday being `0'.

          Leading zeroes are permitted but not required.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

    `%Ow'
          Same as `%w' but using the locale's alternative numeric
          symbols.

    `%W'
          The week number of the current year as a decimal number
          (range `0' through `53').

          Leading zeroes are permitted but not required.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

    `%OW'
          Same as `%W' but using the locale's alternative numeric
          symbols.

    `%x'
          The date using the locale's date format.

    `%Ex'
          Like `%x' but the locale's alternative data representation is
          used.

    `%X'
          The time using the locale's time format.

    `%EX'
          Like `%X' but the locale's alternative time representation is
          used.

    `%y'
          The year without a century as a decimal number (range `0'
          through `99').

          Leading zeroes are permitted but not required.

          Note that it is questionable to use this format without the
          `%C' format.  The `strptime' function does regard input
          values in the range 68 to 99 as the years 1969 to 1999 and
          the values 0 to 68 as the years 2000 to 2068.  But maybe this
          heuristic fails for some input data.

          Therefore it is best to avoid `%y' completely and use `%Y'
          instead.

    `%Ey'
          The offset from `%EC' in the locale's alternative
          representation.

    `%Oy'
          The offset of the year (from `%C') using the locale's
          alternative numeric symbols.

    `%Y'
          The year as a decimal number, using the Gregorian calendar.

    `%EY'
          The full alternative year representation.

    `%z'
          The offset from GMT in ISO 8601/RFC822 format.

    `%Z'
          The timezone name.

          _Note:_ Currently, this is not fully implemented.  The format
          is recognized, input is consumed but no field in TM is set.

    `%%'
          A literal `%' character.

     All other characters in the format string must have a matching
     character in the input string.  Exceptions are white spaces in the
     input string which can match zero or more whitespace characters in
     the format string.

     *Portability Note:* The XPG standard advises applications to use
     at least one whitespace character (as specified by `isspace') or
     other non-alphanumeric characters between any two conversion
     specifications.  The GNU C Library does not have this limitation
     but other libraries might have trouble parsing formats like
     `"%d%m%Y%H%M%S"'.

     The `strptime' function processes the input string from right to
     left.  Each of the three possible input elements (white space,
     literal, or format) are handled one after the other.  If the input
     cannot be matched to the format string the function stops.  The
     remainder of the format and input strings are not processed.

     The function returns a pointer to the first character it was
     unable to process.  If the input string contains more characters
     than required by the format string the return value points right
     after the last consumed input character.  If the whole input
     string is consumed the return value points to the `NULL' byte at
     the end of the string.  If an error occurs, i.e. `strptime' fails
     to match all of the format string, the function returns `NULL'.

   The specification of the function in the XPG standard is rather
vague, leaving out a few important pieces of information.  Most
importantly, it does not specify what happens to those elements of TM
which are not directly initialized by the different formats.  The
implementations on different Unix systems vary here.

   The GNU libc implementation does not touch those fields which are not
directly initialized.  Exceptions are the `tm_wday' and `tm_yday'
elements, which are recomputed if any of the year, month, or date
elements changed.  This has two implications:

   * Before calling the `strptime' function for a new input string, you
     should prepare the TM structure you pass.  Normally this will mean
     initializing all values are to zero.  Alternatively, you can set
     all fields to values like `INT_MAX', allowing you to determine
     which elements were set by the function call.  Zero does not work
     here since it is a valid value for many of the fields.

     Careful initialization is necessary if you want to find out
     whether a certain field in TM was initialized by the function call.

   * You can construct a `struct tm' value with several consecutive
     `strptime' calls.  A useful application of this is e.g. the parsing
     of two separate strings, one containing date information and the
     other time information.  By parsing one after the other without
     clearing the structure in-between, you can construct a complete
     broken-down time.

   The following example shows a function which parses a string which is
contains the date information in either US style or ISO 8601 form:

     const char *
     parse_date (const char *input, struct tm *tm)
     {
       const char *cp;

       /* First clear the result structure.  */
       memset (tm, '\0', sizeof (*tm));

       /* Try the ISO format first.  */
       cp = strptime (input, "%F", tm);
       if (cp == NULL)
         {
           /* Does not match.  Try the US form.  */
           cp = strptime (input, "%D", tm);
         }

       return cp;
     }


File: libc.info,  Node: General Time String Parsing,  Prev: Low-Level Time String Parsing,  Up: Parsing Date and Time

21.4.6.2 A More User-friendly Way to Parse Times and Dates
..........................................................

The Unix standard defines another function for parsing date strings.
The interface is weird, but if the function happens to suit your
application it is just fine.  It is problematic to use this function in
multi-threaded programs or libraries, since it returns a pointer to a
static variable, and uses a global variable and global state (an
environment variable).

 -- Variable: getdate_err
     This variable of type `int' contains the error code of the last
     unsuccessful call to `getdate'.  Defined values are:

    1
          The environment variable `DATEMSK' is not defined or null.

    2
          The template file denoted by the `DATEMSK' environment
          variable cannot be opened.

    3
          Information about the template file cannot retrieved.

    4
          The template file is not a regular file.

    5
          An I/O error occurred while reading the template file.

    6
          Not enough memory available to execute the function.

    7
          The template file contains no matching template.

    8
          The input date is invalid, but would match a template
          otherwise.  This includes dates like February 31st, and dates
          which cannot be represented in a `time_t' variable.

 -- Function: struct tm * getdate (const char *STRING)
     The interface to `getdate' is the simplest possible for a function
     to parse a string and return the value.  STRING is the input
     string and the result is returned in a statically-allocated
     variable.

     The details about how the string is processed are hidden from the
     user.  In fact, they can be outside the control of the program.
     Which formats are recognized is controlled by the file named by
     the environment variable `DATEMSK'.  This file should contain
     lines of valid format strings which could be passed to `strptime'.

     The `getdate' function reads these format strings one after the
     other and tries to match the input string.  The first line which
     completely matches the input string is used.

     Elements not initialized through the format string retain the
     values present at the time of the `getdate' function call.

     The formats recognized by `getdate' are the same as for
     `strptime'.  See above for an explanation.  There are only a few
     extensions to the `strptime' behavior:

        * If the `%Z' format is given the broken-down time is based on
          the current time of the timezone matched, not of the current
          timezone of the runtime environment.

          _Note_: This is not implemented (currently).  The problem is
          that timezone names are not unique.  If a fixed timezone is
          assumed for a given string (say `EST' meaning US East Coast
          time), then uses for countries other than the USA will fail.
          So far we have found no good solution to this.

        * If only the weekday is specified the selected day depends on
          the current date.  If the current weekday is greater or equal
          to the `tm_wday' value the current week's day is chosen,
          otherwise the day next week is chosen.

        * A similar heuristic is used when only the month is given and
          not the year.  If the month is greater than or equal to the
          current month, then the current year is used.  Otherwise it
          wraps to next year.  The first day of the month is assumed if
          one is not explicitly specified.

        * The current hour, minute, and second are used if the
          appropriate value is not set through the format.

        * If no date is given tomorrow's date is used if the time is
          smaller than the current time.  Otherwise today's date is
          taken.

     It should be noted that the format in the template file need not
     only contain format elements.  The following is a list of possible
     format strings (taken from the Unix standard):

          %m
          %A %B %d, %Y %H:%M:%S
          %A
          %B
          %m/%d/%y %I %p
          %d,%m,%Y %H:%M
          at %A the %dst of %B in %Y
          run job at %I %p,%B %dnd
          %A den %d. %B %Y %H.%M Uhr

     As you can see, the template list can contain very specific
     strings like `run job at %I %p,%B %dnd'.  Using the above list of
     templates and assuming the current time is Mon Sep 22 12:19:47 EDT
     1986 we can obtain the following results for the given input.

     Input          Match        Result
     Mon            %a           Mon Sep 22 12:19:47 EDT 1986
     Sun            %a           Sun Sep 28 12:19:47 EDT 1986
     Fri            %a           Fri Sep 26 12:19:47 EDT 1986
     September      %B           Mon Sep 1 12:19:47 EDT 1986
     January        %B           Thu Jan 1 12:19:47 EST 1987
     December       %B           Mon Dec 1 12:19:47 EST 1986
     Sep Mon        %b %a        Mon Sep 1 12:19:47 EDT 1986
     Jan Fri        %b %a        Fri Jan 2 12:19:47 EST 1987
     Dec Mon        %b %a        Mon Dec 1 12:19:47 EST 1986
     Jan Wed 1989   %b %a %Y     Wed Jan 4 12:19:47 EST 1989
     Fri 9          %a %H        Fri Sep 26 09:00:00 EDT 1986
     Feb 10:30      %b %H:%S     Sun Feb 1 10:00:30 EST 1987
     10:30          %H:%M        Tue Sep 23 10:30:00 EDT 1986
     13:30          %H:%M        Mon Sep 22 13:30:00 EDT 1986

     The return value of the function is a pointer to a static variable
     of type `struct tm', or a null pointer if an error occurred.  The
     result is only valid until the next `getdate' call, making this
     function unusable in multi-threaded applications.

     The `errno' variable is _not_ changed.  Error conditions are
     stored in the global variable `getdate_err'.  See the description
     above for a list of the possible error values.

     _Warning:_ The `getdate' function should _never_ be used in
     SUID-programs.  The reason is obvious: using the `DATEMSK'
     environment variable you can get the function to open any
     arbitrary file and chances are high that with some bogus input
     (such as a binary file) the program will crash.

 -- Function: int getdate_r (const char *STRING, struct tm *TP)
     The `getdate_r' function is the reentrant counterpart of
     `getdate'.  It does not use the global variable `getdate_err' to
     signal an error, but instead returns an error code.  The same error
     codes as described in the `getdate_err' documentation above are
     used, with 0 meaning success.

     Moreover, `getdate_r' stores the broken-down time in the variable
     of type `struct tm' pointed to by the second argument, rather than
     in a static variable.

     This function is not defined in the Unix standard.  Nevertheless
     it is available on some other Unix systems as well.

     The warning against using `getdate' in SUID-programs applies to
     `getdate_r' as well.


File: libc.info,  Node: TZ Variable,  Next: Time Zone Functions,  Prev: Parsing Date and Time,  Up: Calendar Time

21.4.7 Specifying the Time Zone with `TZ'
-----------------------------------------

In POSIX systems, a user can specify the time zone by means of the `TZ'
environment variable.  For information about how to set environment
variables, see *Note Environment Variables::.  The functions for
accessing the time zone are declared in `time.h'.  

   You should not normally need to set `TZ'.  If the system is
configured properly, the default time zone will be correct.  You might
set `TZ' if you are using a computer over a network from a different
time zone, and would like times reported to you in the time zone local
to you, rather than what is local to the computer.

   In POSIX.1 systems the value of the `TZ' variable can be in one of
three formats.  With the GNU C library, the most common format is the
last one, which can specify a selection from a large database of time
zone information for many regions of the world.  The first two formats
are used to describe the time zone information directly, which is both
more cumbersome and less precise.  But the POSIX.1 standard only
specifies the details of the first two formats, so it is good to be
familiar with them in case you come across a POSIX.1 system that doesn't
support a time zone information database.

   The first format is used when there is no Daylight Saving Time (or
summer time) in the local time zone:

     STD OFFSET

   The STD string specifies the name of the time zone.  It must be
three or more characters long and must not contain a leading colon,
embedded digits, commas, nor plus and minus signs.  There is no space
character separating the time zone name from the OFFSET, so these
restrictions are necessary to parse the specification correctly.

   The OFFSET specifies the time value you must add to the local time
to get a Coordinated Universal Time value.  It has syntax like
[`+'|`-']HH[`:'MM[`:'SS]].  This is positive if the local time zone is
west of the Prime Meridian and negative if it is east.  The hour must
be between `0' and `23', and the minute and seconds between `0' and
`59'.

   For example, here is how we would specify Eastern Standard Time, but
without any Daylight Saving Time alternative:

     EST+5

   The second format is used when there is Daylight Saving Time:

     STD OFFSET DST [OFFSET]`,'START[`/'TIME]`,'END[`/'TIME]

   The initial STD and OFFSET specify the standard time zone, as
described above.  The DST string and OFFSET specify the name and offset
for the corresponding Daylight Saving Time zone; if the OFFSET is
omitted, it defaults to one hour ahead of standard time.

   The remainder of the specification describes when Daylight Saving
Time is in effect.  The START field is when Daylight Saving Time goes
into effect and the END field is when the change is made back to
standard time.  The following formats are recognized for these fields:

`JN'
     This specifies the Julian day, with N between `1' and `365'.
     February 29 is never counted, even in leap years.

`N'
     This specifies the Julian day, with N between `0' and `365'.
     February 29 is counted in leap years.

`MM.W.D'
     This specifies day D of week W of month M.  The day D must be
     between `0' (Sunday) and `6'.  The week W must be between `1' and
     `5'; week `1' is the first week in which day D occurs, and week
     `5' specifies the _last_ D day in the month.  The month M should be
     between `1' and `12'.

   The TIME fields specify when, in the local time currently in effect,
the change to the other time occurs.  If omitted, the default is
`02:00:00'.

   For example, here is how you would specify the Eastern time zone in
the United States, including the appropriate Daylight Saving Time and
its dates of applicability.  The normal offset from UTC is 5 hours;
since this is west of the prime meridian, the sign is positive.  Summer
time begins on the first Sunday in April at 2:00am, and ends on the
last Sunday in October at 2:00am.

     EST+5EDT,M4.1.0/2,M10.5.0/2

   The schedule of Daylight Saving Time in any particular jurisdiction
has changed over the years.  To be strictly correct, the conversion of
dates and times in the past should be based on the schedule that was in
effect then.  However, this format has no facilities to let you specify
how the schedule has changed from year to year.  The most you can do is
specify one particular schedule--usually the present day schedule--and
this is used to convert any date, no matter when.  For precise time zone
specifications, it is best to use the time zone information database
(see below).

   The third format looks like this:

     :CHARACTERS

   Each operating system interprets this format differently; in the GNU
C library, CHARACTERS is the name of a file which describes the time
zone.

   If the `TZ' environment variable does not have a value, the
operation chooses a time zone by default.  In the GNU C library, the
default time zone is like the specification `TZ=:/etc/localtime' (or
`TZ=:/usr/local/etc/localtime', depending on how GNU C library was
configured; *note Installation::).  Other C libraries use their own
rule for choosing the default time zone, so there is little we can say
about them.

   If CHARACTERS begins with a slash, it is an absolute file name;
otherwise the library looks for the file
`/share/lib/zoneinfo/CHARACTERS'.  The `zoneinfo' directory contains
data files describing local time zones in many different parts of the
world.  The names represent major cities, with subdirectories for
geographical areas; for example, `America/New_York', `Europe/London',
`Asia/Hong_Kong'.  These data files are installed by the system
administrator, who also sets `/etc/localtime' to point to the data file
for the local time zone.  The GNU C library comes with a large database
of time zone information for most regions of the world, which is
maintained by a community of volunteers and put in the public domain.


File: libc.info,  Node: Time Zone Functions,  Next: Time Functions Example,  Prev: TZ Variable,  Up: Calendar Time

21.4.8 Functions and Variables for Time Zones
---------------------------------------------

 -- Variable: char * tzname [2]
     The array `tzname' contains two strings, which are the standard
     names of the pair of time zones (standard and Daylight Saving)
     that the user has selected.  `tzname[0]' is the name of the
     standard time zone (for example, `"EST"'), and `tzname[1]' is the
     name for the time zone when Daylight Saving Time is in use (for
     example, `"EDT"').  These correspond to the STD and DST strings
     (respectively) from the `TZ' environment variable.  If Daylight
     Saving Time is never used, `tzname[1]' is the empty string.

     The `tzname' array is initialized from the `TZ' environment
     variable whenever `tzset', `ctime', `strftime', `mktime', or
     `localtime' is called.  If multiple abbreviations have been used
     (e.g. `"EWT"' and `"EDT"' for U.S. Eastern War Time and Eastern
     Daylight Time), the array contains the most recent abbreviation.

     The `tzname' array is required for POSIX.1 compatibility, but in
     GNU programs it is better to use the `tm_zone' member of the
     broken-down time structure, since `tm_zone' reports the correct
     abbreviation even when it is not the latest one.

     Though the strings are declared as `char *' the user must refrain
     from modifying these strings.  Modifying the strings will almost
     certainly lead to trouble.


 -- Function: void tzset (void)
     The `tzset' function initializes the `tzname' variable from the
     value of the `TZ' environment variable.  It is not usually
     necessary for your program to call this function, because it is
     called automatically when you use the other time conversion
     functions that depend on the time zone.

   The following variables are defined for compatibility with System V
Unix.  Like `tzname', these variables are set by calling `tzset' or the
other time conversion functions.

 -- Variable: long int timezone
     This contains the difference between UTC and the latest local
     standard time, in seconds west of UTC.  For example, in the U.S.
     Eastern time zone, the value is `5*60*60'.  Unlike the `tm_gmtoff'
     member of the broken-down time structure, this value is not
     adjusted for daylight saving, and its sign is reversed.  In GNU
     programs it is better to use `tm_gmtoff', since it contains the
     correct offset even when it is not the latest one.

 -- Variable: int daylight
     This variable has a nonzero value if Daylight Saving Time rules
     apply.  A nonzero value does not necessarily mean that Daylight
     Saving Time is now in effect; it means only that Daylight Saving
     Time is sometimes in effect.


File: libc.info,  Node: Time Functions Example,  Prev: Time Zone Functions,  Up: Calendar Time

21.4.9 Time Functions Example
-----------------------------

Here is an example program showing the use of some of the calendar time
functions.

     #include <time.h>
     #include <stdio.h>

     #define SIZE 256

     int
     main (void)
     {
       char buffer[SIZE];
       time_t curtime;
       struct tm *loctime;

       /* Get the current time. */
       curtime = time (NULL);

       /* Convert it to local time representation. */
       loctime = localtime (&curtime);

       /* Print out the date and time in the standard format. */
       fputs (asctime (loctime), stdout);

       /* Print it out in a nice format. */
       strftime (buffer, SIZE, "Today is %A, %B %d.\n", loctime);
       fputs (buffer, stdout);
       strftime (buffer, SIZE, "The time is %I:%M %p.\n", loctime);
       fputs (buffer, stdout);

       return 0;
     }

   It produces output like this:

     Wed Jul 31 13:02:36 1991
     Today is Wednesday, July 31.
     The time is 01:02 PM.


File: libc.info,  Node: Setting an Alarm,  Next: Sleeping,  Prev: Calendar Time,  Up: Date and Time

21.5 Setting an Alarm
=====================

The `alarm' and `setitimer' functions provide a mechanism for a process
to interrupt itself in the future.  They do this by setting a timer;
when the timer expires, the process receives a signal.

   Each process has three independent interval timers available:

   * A real-time timer that counts elapsed time.  This timer sends a
     `SIGALRM' signal to the process when it expires.  

   * A virtual timer that counts processor time used by the process.
     This timer sends a `SIGVTALRM' signal to the process when it
     expires.  

   * A profiling timer that counts both processor time used by the
     process, and processor time spent in system calls on behalf of the
     process.  This timer sends a `SIGPROF' signal to the process when
     it expires.  

     This timer is useful for profiling in interpreters.  The interval
     timer mechanism does not have the fine granularity necessary for
     profiling native code.

   You can only have one timer of each kind set at any given time.  If
you set a timer that has not yet expired, that timer is simply reset to
the new value.

   You should establish a handler for the appropriate alarm signal using
`signal' or `sigaction' before issuing a call to `setitimer' or
`alarm'.  Otherwise, an unusual chain of events could cause the timer
to expire before your program establishes the handler.  In this case it
would be terminated, since termination is the default action for the
alarm signals.  *Note Signal Handling::.

   To be able to use the alarm function to interrupt a system call which
might block otherwise indefinitely it is important to _not_ set the
`SA_RESTART' flag when registering the signal handler using
`sigaction'.  When not using `sigaction' things get even uglier: the
`signal' function has to fixed semantics with respect to restarts.  The
BSD semantics for this function is to set the flag.  Therefore, if
`sigaction' for whatever reason cannot be used, it is necessary to use
`sysv_signal' and not `signal'.

   The `setitimer' function is the primary means for setting an alarm.
This facility is declared in the header file `sys/time.h'.  The `alarm'
function, declared in `unistd.h', provides a somewhat simpler interface
for setting the real-time timer.  

 -- Data Type: struct itimerval
     This structure is used to specify when a timer should expire.  It
     contains the following members:
    `struct timeval it_interval'
          This is the period between successive timer interrupts.  If
          zero, the alarm will only be sent once.

    `struct timeval it_value'
          This is the period between now and the first timer interrupt.
          If zero, the alarm is disabled.

     The `struct timeval' data type is described in *Note Elapsed
     Time::.

 -- Function: int setitimer (int WHICH, struct itimerval *NEW, struct
          itimerval *OLD)
     The `setitimer' function sets the timer specified by WHICH
     according to NEW.  The WHICH argument can have a value of
     `ITIMER_REAL', `ITIMER_VIRTUAL', or `ITIMER_PROF'.

     If OLD is not a null pointer, `setitimer' returns information
     about any previous unexpired timer of the same kind in the
     structure it points to.

     The return value is `0' on success and `-1' on failure.  The
     following `errno' error conditions are defined for this function:

    `EINVAL'
          The timer period is too large.

 -- Function: int getitimer (int WHICH, struct itimerval *OLD)
     The `getitimer' function stores information about the timer
     specified by WHICH in the structure pointed at by OLD.

     The return value and error conditions are the same as for
     `setitimer'.

`ITIMER_REAL'
     This constant can be used as the WHICH argument to the `setitimer'
     and `getitimer' functions to specify the real-time timer.

`ITIMER_VIRTUAL'
     This constant can be used as the WHICH argument to the `setitimer'
     and `getitimer' functions to specify the virtual timer.

`ITIMER_PROF'
     This constant can be used as the WHICH argument to the `setitimer'
     and `getitimer' functions to specify the profiling timer.

 -- Function: unsigned int alarm (unsigned int SECONDS)
     The `alarm' function sets the real-time timer to expire in SECONDS
     seconds.  If you want to cancel any existing alarm, you can do
     this by calling `alarm' with a SECONDS argument of zero.

     The return value indicates how many seconds remain before the
     previous alarm would have been sent.  If there is no previous
     alarm, `alarm' returns zero.

   The `alarm' function could be defined in terms of `setitimer' like
this:

     unsigned int
     alarm (unsigned int seconds)
     {
       struct itimerval old, new;
       new.it_interval.tv_usec = 0;
       new.it_interval.tv_sec = 0;
       new.it_value.tv_usec = 0;
       new.it_value.tv_sec = (long int) seconds;
       if (setitimer (ITIMER_REAL, &new, &old) < 0)
         return 0;
       else
         return old.it_value.tv_sec;
     }

   There is an example showing the use of the `alarm' function in *Note
Handler Returns::.

   If you simply want your process to wait for a given number of
seconds, you should use the `sleep' function.  *Note Sleeping::.

   You shouldn't count on the signal arriving precisely when the timer
expires.  In a multiprocessing environment there is typically some
amount of delay involved.

   *Portability Note:* The `setitimer' and `getitimer' functions are
derived from BSD Unix, while the `alarm' function is specified by the
POSIX.1 standard.  `setitimer' is more powerful than `alarm', but
`alarm' is more widely used.


File: libc.info,  Node: Sleeping,  Prev: Setting an Alarm,  Up: Date and Time

21.6 Sleeping
=============

The function `sleep' gives a simple way to make the program wait for a
short interval.  If your program doesn't use signals (except to
terminate), then you can expect `sleep' to wait reliably throughout the
specified interval.  Otherwise, `sleep' can return sooner if a signal
arrives; if you want to wait for a given interval regardless of
signals, use `select' (*note Waiting for I/O::) and don't specify any
descriptors to wait for.

 -- Function: unsigned int sleep (unsigned int SECONDS)
     The `sleep' function waits for SECONDS or until a signal is
     delivered, whichever happens first.

     If `sleep' function returns because the requested interval is over,
     it returns a value of zero.  If it returns because of delivery of a
     signal, its return value is the remaining time in the sleep
     interval.

     The `sleep' function is declared in `unistd.h'.

   Resist the temptation to implement a sleep for a fixed amount of
time by using the return value of `sleep', when nonzero, to call
`sleep' again.  This will work with a certain amount of accuracy as
long as signals arrive infrequently.  But each signal can cause the
eventual wakeup time to be off by an additional second or so.  Suppose a
few signals happen to arrive in rapid succession by bad luck--there is
no limit on how much this could shorten or lengthen the wait.

   Instead, compute the calendar time at which the program should stop
waiting, and keep trying to wait until that calendar time.  This won't
be off by more than a second.  With just a little more work, you can use
`select' and make the waiting period quite accurate.  (Of course, heavy
system load can cause additional unavoidable delays--unless the machine
is dedicated to one application, there is no way you can avoid this.)

   On some systems, `sleep' can do strange things if your program uses
`SIGALRM' explicitly.  Even if `SIGALRM' signals are being ignored or
blocked when `sleep' is called, `sleep' might return prematurely on
delivery of a `SIGALRM' signal.  If you have established a handler for
`SIGALRM' signals and a `SIGALRM' signal is delivered while the process
is sleeping, the action taken might be just to cause `sleep' to return
instead of invoking your handler.  And, if `sleep' is interrupted by
delivery of a signal whose handler requests an alarm or alters the
handling of `SIGALRM', this handler and `sleep' will interfere.

   On the GNU system, it is safe to use `sleep' and `SIGALRM' in the
same program, because `sleep' does not work by means of `SIGALRM'.

 -- Function: int nanosleep (const struct timespec *REQUESTED_TIME,
          struct timespec *REMAINING)
     If resolution to seconds is not enough the `nanosleep' function can
     be used.  As the name suggests the sleep interval can be specified
     in nanoseconds.  The actual elapsed time of the sleep interval
     might be longer since the system rounds the elapsed time you
     request up to the next integer multiple of the actual resolution
     the system can deliver.

     *`requested_time' is the elapsed time of the interval you want to
     sleep.

     The function returns as *`remaining' the elapsed time left in the
     interval for which you requested to sleep.  If the interval
     completed without getting interrupted by a signal, this is zero.

     `struct timespec' is described in *Note Elapsed Time::.

     If the function returns because the interval is over the return
     value is zero.  If the function returns -1 the global variable
     ERRNO is set to the following values:

    `EINTR'
          The call was interrupted because a signal was delivered to
          the thread.  If the REMAINING parameter is not the null
          pointer the structure pointed to by REMAINING is updated to
          contain the remaining elapsed time.

    `EINVAL'
          The nanosecond value in the REQUESTED_TIME parameter contains
          an illegal value.  Either the value is negative or greater
          than or equal to 1000 million.

     This function is a cancellation point in multi-threaded programs.
     This is a problem if the thread allocates some resources (like
     memory, file descriptors, semaphores or whatever) at the time
     `nanosleep' is called.  If the thread gets canceled these
     resources stay allocated until the program ends.  To avoid this
     calls to `nanosleep' should be protected using cancellation
     handlers.

     The `nanosleep' function is declared in `time.h'.


File: libc.info,  Node: Resource Usage And Limitation,  Next: Non-Local Exits,  Prev: Date and Time,  Up: Top

22 Resource Usage And Limitation
********************************

This chapter describes functions for examining how much of various
kinds of resources (CPU time, memory, etc.) a process has used and
getting and setting limits on future usage.

* Menu:

* Resource Usage::		Measuring various resources used.
* Limits on Resources::		Specifying limits on resource usage.
* Priority::			Reading or setting process run priority.
* Memory Resources::            Querying memory available resources.
* Processor Resources::         Learn about the processors available.


File: libc.info,  Node: Resource Usage,  Next: Limits on Resources,  Up: Resource Usage And Limitation

22.1 Resource Usage
===================

The function `getrusage' and the data type `struct rusage' are used to
examine the resource usage of a process.  They are declared in
`sys/resource.h'.

 -- Function: int getrusage (int PROCESSES, struct rusage *RUSAGE)
     This function reports resource usage totals for processes
     specified by PROCESSES, storing the information in `*RUSAGE'.

     In most systems, PROCESSES has only two valid values:

    `RUSAGE_SELF'
          Just the current process.

    `RUSAGE_CHILDREN'
          All child processes (direct and indirect) that have already
          terminated.

     In the GNU system, you can also inquire about a particular child
     process by specifying its process ID.

     The return value of `getrusage' is zero for success, and `-1' for
     failure.

    `EINVAL'
          The argument PROCESSES is not valid.

   One way of getting resource usage for a particular child process is
with the function `wait4', which returns totals for a child when it
terminates.  *Note BSD Wait Functions::.

 -- Data Type: struct rusage
     This data type stores various resource usage statistics.  It has
     the following members, and possibly others:

    `struct timeval ru_utime'
          Time spent executing user instructions.

    `struct timeval ru_stime'
          Time spent in operating system code on behalf of PROCESSES.

    `long int ru_maxrss'
          The maximum resident set size used, in kilobytes.  That is,
          the maximum number of kilobytes of physical memory that
          PROCESSES used simultaneously.

    `long int ru_ixrss'
          An integral value expressed in kilobytes times ticks of
          execution, which indicates the amount of memory used by text
          that was shared with other processes.

    `long int ru_idrss'
          An integral value expressed the same way, which is the amount
          of unshared memory used for data.

    `long int ru_isrss'
          An integral value expressed the same way, which is the amount
          of unshared memory used for stack space.

    `long int ru_minflt'
          The number of page faults which were serviced without
          requiring any I/O.

    `long int ru_majflt'
          The number of page faults which were serviced by doing I/O.

    `long int ru_nswap'
          The number of times PROCESSES was swapped entirely out of
          main memory.

    `long int ru_inblock'
          The number of times the file system had to read from the disk
          on behalf of PROCESSES.

    `long int ru_oublock'
          The number of times the file system had to write to the disk
          on behalf of PROCESSES.

    `long int ru_msgsnd'
          Number of IPC messages sent.

    `long int ru_msgrcv'
          Number of IPC messages received.

    `long int ru_nsignals'
          Number of signals received.

    `long int ru_nvcsw'
          The number of times PROCESSES voluntarily invoked a context
          switch (usually to wait for some service).

    `long int ru_nivcsw'
          The number of times an involuntary context switch took place
          (because a time slice expired, or another process of higher
          priority was scheduled).

   `vtimes' is a historical function that does some of what `getrusage'
does.  `getrusage' is a better choice.

   `vtimes' and its `vtimes' data structure are declared in
`sys/vtimes.h'.  

 -- Function: int vtimes (struct vtimes CURRENT, struct vtimes CHILD)
     `vtimes' reports resource usage totals for a process.

     If CURRENT is non-null, `vtimes' stores resource usage totals for
     the invoking process alone in the structure to which it points.  If
     CHILD is non-null, `vtimes' stores resource usage totals for all
     past children (which have terminated) of the invoking process in
     the structure to which it points.

      -- Data Type: struct vtimes
          This data type contains information about the resource usage
          of a process.  Each member corresponds to a member of the
          `struct rusage' data type described above.

         `vm_utime'
               User CPU time.  Analogous to `ru_utime' in `struct
               rusage'

         `vm_stime'
               System CPU time.  Analogous to `ru_stime' in `struct
               rusage'

         `vm_idsrss'
               Data and stack memory.  The sum of the values that would
               be reported as `ru_idrss' and `ru_isrss' in `struct
               rusage'

         `vm_ixrss'
               Shared memory.  Analogous to `ru_ixrss' in `struct
               rusage'

         `vm_maxrss'
               Maximent resident set size.  Analogous to `ru_maxrss' in
               `struct rusage'

         `vm_majflt'
               Major page faults.  Analogous to `ru_majflt' in `struct
               rusage'

         `vm_minflt'
               Minor page faults.  Analogous to `ru_minflt' in `struct
               rusage'

         `vm_nswap'
               Swap count.  Analogous to `ru_nswap' in `struct rusage'

         `vm_inblk'
               Disk reads.  Analogous to `ru_inblk' in `struct rusage'

         `vm_oublk'
               Disk writes.  Analogous to `ru_oublk' in `struct rusage'

     The return value is zero if the function succeeds; `-1' otherwise.

   An additional historical function for examining resource usage,
`vtimes', is supported but not documented here.  It is declared in
`sys/vtimes.h'.


File: libc.info,  Node: Limits on Resources,  Next: Priority,  Prev: Resource Usage,  Up: Resource Usage And Limitation

22.2 Limiting Resource Usage
============================

You can specify limits for the resource usage of a process.  When the
process tries to exceed a limit, it may get a signal, or the system call
by which it tried to do so may fail, depending on the resource.  Each
process initially inherits its limit values from its parent, but it can
subsequently change them.

   There are two per-process limits associated with a resource: 

"current limit"
     The current limit is the value the system will not allow usage to
     exceed.  It is also called the "soft limit" because the process
     being limited can generally raise the current limit at will.  

"maximum limit"
     The maximum limit is the maximum value to which a process is
     allowed to set its current limit.  It is also called the "hard
     limit" because there is no way for a process to get around it.  A
     process may lower its own maximum limit, but only the superuser
     may increase a maximum limit.  

   The symbols for use with `getrlimit', `setrlimit', `getrlimit64',
and `setrlimit64' are defined in `sys/resource.h'.

 -- Function: int getrlimit (int RESOURCE, struct rlimit *RLP)
     Read the current and maximum limits for the resource RESOURCE and
     store them in `*RLP'.

     The return value is `0' on success and `-1' on failure.  The only
     possible `errno' error condition is `EFAULT'.

     When the sources are compiled with `_FILE_OFFSET_BITS == 64' on a
     32-bit system this function is in fact `getrlimit64'.  Thus, the
     LFS interface transparently replaces the old interface.

 -- Function: int getrlimit64 (int RESOURCE, struct rlimit64 *RLP)
     This function is similar to `getrlimit' but its second parameter is
     a pointer to a variable of type `struct rlimit64', which allows it
     to read values which wouldn't fit in the member of a `struct
     rlimit'.

     If the sources are compiled with `_FILE_OFFSET_BITS == 64' on a
     32-bit machine, this function is available under the name
     `getrlimit' and so transparently replaces the old interface.

 -- Function: int setrlimit (int RESOURCE, const struct rlimit *RLP)
     Store the current and maximum limits for the resource RESOURCE in
     `*RLP'.

     The return value is `0' on success and `-1' on failure.  The
     following `errno' error condition is possible:

    `EPERM'
             * The process tried to raise a current limit beyond the
               maximum limit.

             * The process tried to raise a maximum limit, but is not
               superuser.

     When the sources are compiled with `_FILE_OFFSET_BITS == 64' on a
     32-bit system this function is in fact `setrlimit64'.  Thus, the
     LFS interface transparently replaces the old interface.

 -- Function: int setrlimit64 (int RESOURCE, const struct rlimit64 *RLP)
     This function is similar to `setrlimit' but its second parameter is
     a pointer to a variable of type `struct rlimit64' which allows it
     to set values which wouldn't fit in the member of a `struct
     rlimit'.

     If the sources are compiled with `_FILE_OFFSET_BITS == 64' on a
     32-bit machine this function is available under the name
     `setrlimit' and so transparently replaces the old interface.

 -- Data Type: struct rlimit
     This structure is used with `getrlimit' to receive limit values,
     and with `setrlimit' to specify limit values for a particular
     process and resource.  It has two fields:

    `rlim_t rlim_cur'
          The current limit

    `rlim_t rlim_max'
          The maximum limit.

     For `getrlimit', the structure is an output; it receives the
     current values.  For `setrlimit', it specifies the new values.

   For the LFS functions a similar type is defined in `sys/resource.h'.

 -- Data Type: struct rlimit64
     This structure is analogous to the `rlimit' structure above, but
     its components have wider ranges.  It has two fields:

    `rlim64_t rlim_cur'
          This is analogous to `rlimit.rlim_cur', but with a different
          type.

    `rlim64_t rlim_max'
          This is analogous to `rlimit.rlim_max', but with a different
          type.


   Here is a list of resources for which you can specify a limit.
Memory and file sizes are measured in bytes.

`RLIMIT_CPU'
     The maximum amount of CPU time the process can use.  If it runs for
     longer than this, it gets a signal: `SIGXCPU'.  The value is
     measured in seconds.  *Note Operation Error Signals::.

`RLIMIT_FSIZE'
     The maximum size of file the process can create.  Trying to write a
     larger file causes a signal: `SIGXFSZ'.  *Note Operation Error
     Signals::.

`RLIMIT_DATA'
     The maximum size of data memory for the process.  If the process
     tries to allocate data memory beyond this amount, the allocation
     function fails.

`RLIMIT_STACK'
     The maximum stack size for the process.  If the process tries to
     extend its stack past this size, it gets a `SIGSEGV' signal.
     *Note Program Error Signals::.

`RLIMIT_CORE'
     The maximum size core file that this process can create.  If the
     process terminates and would dump a core file larger than this,
     then no core file is created.  So setting this limit to zero
     prevents core files from ever being created.

`RLIMIT_RSS'
     The maximum amount of physical memory that this process should get.
     This parameter is a guide for the system's scheduler and memory
     allocator; the system may give the process more memory when there
     is a surplus.

`RLIMIT_MEMLOCK'
     The maximum amount of memory that can be locked into physical
     memory (so it will never be paged out).

`RLIMIT_NPROC'
     The maximum number of processes that can be created with the same
     user ID.  If you have reached the limit for your user ID, `fork'
     will fail with `EAGAIN'.  *Note Creating a Process::.

`RLIMIT_NOFILE'
`RLIMIT_OFILE'
     The maximum number of files that the process can open.  If it
     tries to open more files than this, its open attempt fails with
     `errno' `EMFILE'.  *Note Error Codes::.  Not all systems support
     this limit; GNU does, and 4.4 BSD does.

`RLIMIT_AS'
     The maximum size of total memory that this process should get.  If
     the process tries to allocate more memory beyond this amount with,
     for example, `brk', `malloc', `mmap' or `sbrk', the allocation
     function fails.

`RLIM_NLIMITS'
     The number of different resource limits.  Any valid RESOURCE
     operand must be less than `RLIM_NLIMITS'.

 -- Constant: int RLIM_INFINITY
     This constant stands for a value of "infinity" when supplied as
     the limit value in `setrlimit'.

   The following are historical functions to do some of what the
functions above do.  The functions above are better choices.

   `ulimit' and the command symbols are declared in `ulimit.h'.  

 -- Function: int ulimit (int CMD, ...)
     `ulimit' gets the current limit or sets the current and maximum
     limit for a particular resource for the calling process according
     to the command CMD.a

     If you are getting a limit, the command argument is the only
     argument.  If you are setting a limit, there is a second argument:
     `long int' LIMIT which is the value to which you are setting the
     limit.

     The CMD values and the operations they specify are:
    `GETFSIZE'
          Get the current limit on the size of a file, in units of 512
          bytes.

    `SETFSIZE'
          Set the current and maximum limit on the size of a file to
          LIMIT * 512 bytes.


     There are also some other CMD values that may do things on some
     systems, but they are not supported.

     Only the superuser may increase a maximum limit.

     When you successfully get a limit, the return value of `ulimit' is
     that limit, which is never negative.  When you successfully set a
     limit, the return value is zero.  When the function fails, the
     return value is `-1' and `errno' is set according to the reason:

    `EPERM'
          A process tried to increase a maximum limit, but is not
          superuser.


   `vlimit' and its resource symbols are declared in `sys/vlimit.h'.  

 -- Function: int vlimit (int RESOURCE, int LIMIT)
     `vlimit' sets the current limit for a resource for a process.

     RESOURCE identifies the resource:

    `LIM_CPU'
          Maximum CPU time.  Same as `RLIMIT_CPU' for `setrlimit'.

    `LIM_FSIZE'
          Maximum file size.  Same as `RLIMIT_FSIZE' for `setrlimit'.

    `LIM_DATA'
          Maximum data memory.  Same as `RLIMIT_DATA' for `setrlimit'.

    `LIM_STACK'
          Maximum stack size.  Same as `RLIMIT_STACK' for `setrlimit'.

    `LIM_CORE'
          Maximum core file size.  Same as `RLIMIT_COR' for `setrlimit'.

    `LIM_MAXRSS'
          Maximum physical memory.  Same as `RLIMIT_RSS' for
          `setrlimit'.

     The return value is zero for success, and `-1' with `errno' set
     accordingly for failure:

    `EPERM'
          The process tried to set its current limit beyond its maximum
          limit.



File: libc.info,  Node: Priority,  Next: Memory Resources,  Prev: Limits on Resources,  Up: Resource Usage And Limitation

22.3 Process CPU Priority And Scheduling
========================================

When multiple processes simultaneously require CPU time, the system's
scheduling policy and process CPU priorities determine which processes
get it.  This section describes how that determination is made and GNU
C library functions to control it.

   It is common to refer to CPU scheduling simply as scheduling and a
process' CPU priority simply as the process' priority, with the CPU
resource being implied.  Bear in mind, though, that CPU time is not the
only resource a process uses or that processes contend for.  In some
cases, it is not even particularly important.  Giving a process a high
"priority" may have very little effect on how fast a process runs with
respect to other processes.  The priorities discussed in this section
apply only to CPU time.

   CPU scheduling is a complex issue and different systems do it in
wildly different ways.  New ideas continually develop and find their
way into the intricacies of the various systems' scheduling algorithms.
This section discusses the general concepts, some specifics of systems
that commonly use the GNU C library, and some standards.

   For simplicity, we talk about CPU contention as if there is only one
CPU in the system.  But all the same principles apply when a processor
has multiple CPUs, and knowing that the number of processes that can
run at any one time is equal to the number of CPUs, you can easily
extrapolate the information.

   The functions described in this section are all defined by the
POSIX.1 and POSIX.1b standards (the `sched...' functions are POSIX.1b).
However, POSIX does not define any semantics for the values that these
functions get and set.  In this chapter, the semantics are based on the
Linux kernel's implementation of the POSIX standard.  As you will see,
the Linux implementation is quite the inverse of what the authors of the
POSIX syntax had in mind.

* Menu:

* Absolute Priority::               The first tier of priority.  Posix
* Realtime Scheduling::             Scheduling among the process nobility
* Basic Scheduling Functions::      Get/set scheduling policy, priority
* Traditional Scheduling::          Scheduling among the vulgar masses
* CPU Affinity::                    Limiting execution to certain CPUs


File: libc.info,  Node: Absolute Priority,  Next: Realtime Scheduling,  Up: Priority

22.3.1 Absolute Priority
------------------------

Every process has an absolute priority, and it is represented by a
number.  The higher the number, the higher the absolute priority.

   On systems of the past, and most systems today, all processes have
absolute priority 0 and this section is irrelevant.  In that case,
*Note Traditional Scheduling::.  Absolute priorities were invented to
accommodate realtime systems, in which it is vital that certain
processes be able to respond to external events happening in real time,
which means they cannot wait around while some other process that _wants
to_, but doesn't _need to_ run occupies the CPU.

   When two processes are in contention to use the CPU at any instant,
the one with the higher absolute priority always gets it.  This is true
even if the process with the lower priority is already using the CPU
(i.e. the scheduling is preemptive).  Of course, we're only talking
about processes that are running or "ready to run," which means they are
ready to execute instructions right now.  When a process blocks to wait
for something like I/O, its absolute priority is irrelevant.

   *Note_*  The term "runnable" is a synonym for "ready to run."

   When two processes are running or ready to run and both have the same
absolute priority, it's more interesting.  In that case, who gets the
CPU is determined by the scheduling policy.  If the processes have
absolute priority 0, the traditional scheduling policy described in
*Note Traditional Scheduling:: applies.  Otherwise, the policies
described in *Note Realtime Scheduling:: apply.

   You normally give an absolute priority above 0 only to a process that
can be trusted not to hog the CPU.  Such processes are designed to block
(or terminate) after relatively short CPU runs.

   A process begins life with the same absolute priority as its parent
process.  Functions described in *Note Basic Scheduling Functions:: can
change it.

   Only a privileged process can change a process' absolute priority to
something other than `0'.  Only a privileged process or the target
process' owner can change its absolute priority at all.

   POSIX requires absolute priority values used with the realtime
scheduling policies to be consecutive with a range of at least 32.  On
Linux, they are 1 through 99.  The functions `sched_get_priority_max'
and `sched_set_priority_min' portably tell you what the range is on a
particular system.

22.3.1.1 Using Absolute Priority
................................

One thing you must keep in mind when designing real time applications is
that having higher absolute priority than any other process doesn't
guarantee the process can run continuously.  Two things that can wreck a
good CPU run are interrupts and page faults.

   Interrupt handlers live in that limbo between processes.  The CPU is
executing instructions, but they aren't part of any process.  An
interrupt will stop even the highest priority process.  So you must
allow for slight delays and make sure that no device in the system has
an interrupt handler that could cause too long a delay between
instructions for your process.

   Similarly, a page fault causes what looks like a straightforward
sequence of instructions to take a long time.  The fact that other
processes get to run while the page faults in is of no consequence,
because as soon as the I/O is complete, the high priority process will
kick them out and run again, but the wait for the I/O itself could be a
problem.  To neutralize this threat, use `mlock' or `mlockall'.

   There are a few ramifications of the absoluteness of this priority
on a single-CPU system that you need to keep in mind when you choose to
set a priority and also when you're working on a program that runs with
high absolute priority.  Consider a process that has higher absolute
priority than any other process in the system and due to a bug in its
program, it gets into an infinite loop.  It will never cede the CPU.
You can't run a command to kill it because your command would need to
get the CPU in order to run.  The errant program is in complete
control.  It controls the vertical, it controls the horizontal.

   There are two ways to avoid this: 1) keep a shell running somewhere
with a higher absolute priority.  2) keep a controlling terminal
attached to the high priority process group.  All the priority in the
world won't stop an interrupt handler from running and delivering a
signal to the process if you hit Control-C.

   Some systems use absolute priority as a means of allocating a fixed
percentage of CPU time to a process.  To do this, a super high priority
privileged process constantly monitors the process' CPU usage and raises
its absolute priority when the process isn't getting its entitled share
and lowers it when the process is exceeding it.

   *Note_*  The absolute priority is sometimes called the "static
priority."  We don't use that term in this manual because it misses the
most important feature of the absolute priority:  its absoluteness.


File: libc.info,  Node: Realtime Scheduling,  Next: Basic Scheduling Functions,  Prev: Absolute Priority,  Up: Priority

22.3.2 Realtime Scheduling
--------------------------

Whenever two processes with the same absolute priority are ready to run,
the kernel has a decision to make, because only one can run at a time.
If the processes have absolute priority 0, the kernel makes this
decision as described in *Note Traditional Scheduling::.  Otherwise,
the decision is as described in this section.

   If two processes are ready to run but have different absolute
priorities, the decision is much simpler, and is described in *Note
Absolute Priority::.

   Each process has a scheduling policy.  For processes with absolute
priority other than zero, there are two available:

  1. First Come First Served

  2. Round Robin

   The most sensible case is where all the processes with a certain
absolute priority have the same scheduling policy.  We'll discuss that
first.

   In Round Robin, processes share the CPU, each one running for a small
quantum of time ("time slice") and then yielding to another in a
circular fashion.  Of course, only processes that are ready to run and
have the same absolute priority are in this circle.

   In First Come First Served, the process that has been waiting the
longest to run gets the CPU, and it keeps it until it voluntarily
relinquishes the CPU, runs out of things to do (blocks), or gets
preempted by a higher priority process.

   First Come First Served, along with maximal absolute priority and
careful control of interrupts and page faults, is the one to use when a
process absolutely, positively has to run at full CPU speed or not at
all.

   Judicious use of `sched_yield' function invocations by processes
with First Come First Served scheduling policy forms a good compromise
between Round Robin and First Come First Served.

   To understand how scheduling works when processes of different
scheduling policies occupy the same absolute priority, you have to know
the nitty gritty details of how processes enter and exit the ready to
run list:

   In both cases, the ready to run list is organized as a true queue,
where a process gets pushed onto the tail when it becomes ready to run
and is popped off the head when the scheduler decides to run it.  Note
that ready to run and running are two mutually exclusive states.  When
the scheduler runs a process, that process is no longer ready to run
and no longer in the ready to run list.  When the process stops
running, it may go back to being ready to run again.

   The only difference between a process that is assigned the Round
Robin scheduling policy and a process that is assigned First Come First
Serve is that in the former case, the process is automatically booted
off the CPU after a certain amount of time.  When that happens, the
process goes back to being ready to run, which means it enters the
queue at the tail.  The time quantum we're talking about is small.
Really small.  This is not your father's timesharing.  For example,
with the Linux kernel, the round robin time slice is a thousand times
shorter than its typical time slice for traditional scheduling.

   A process begins life with the same scheduling policy as its parent
process.  Functions described in *Note Basic Scheduling Functions:: can
change it.

   Only a privileged process can set the scheduling policy of a process
that has absolute priority higher than 0.

