Embedded_AI/gcc-linaro-7.5.0-2019.12-x86_64_arm-linux-gnueabihf/arm-linux-gnueabihf/libc/usr/share/info/libc.info-8

This is libc.info, produced by makeinfo version 5.2 from libc.texinfo.

This file documents the GNU C Library.

   This is ‘The GNU C Library Reference Manual’, for version 2.25.

   Copyright © 1993–2017 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 1.3 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 GNU
Manual”, and with the Back-Cover Texts as in (a) below.  A copy of the
license is included in the section entitled "GNU Free Documentation
License".

   (a) The FSF’s Back-Cover Text is: “You have the freedom to copy and
modify this GNU manual.  Buying copies from the FSF supports it in
developing GNU and promoting software freedom.”
INFO-DIR-SECTION Software 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
* a64l: (libc)Encode Binary Data.
* abort: (libc)Aborting a Program.
* abs: (libc)Absolute Value.
* accept: (libc)Accepting Connections.
* access: (libc)Testing File Access.
* acosf: (libc)Inverse Trig Functions.
* acoshf: (libc)Hyperbolic Functions.
* acosh: (libc)Hyperbolic Functions.
* acoshl: (libc)Hyperbolic Functions.
* acos: (libc)Inverse Trig 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.
* aligned_alloc: (libc)Aligned Memory Blocks.
* alloca: (libc)Variable Size Automatic.
* alphasort64: (libc)Scanning Directory Content.
* alphasort: (libc)Scanning Directory Content.
* ALTWERASE: (libc)Local Modes.
* ARG_MAX: (libc)General Limits.
* argp_error: (libc)Argp Helper Functions.
* ARGP_ERR_UNKNOWN: (libc)Argp Parser 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.
* asinf: (libc)Inverse Trig Functions.
* asinhf: (libc)Hyperbolic Functions.
* asinh: (libc)Hyperbolic Functions.
* asinhl: (libc)Hyperbolic Functions.
* asin: (libc)Inverse Trig Functions.
* asinl: (libc)Inverse Trig Functions.
* asprintf: (libc)Dynamic Output.
* assert: (libc)Consistency Checking.
* assert_perror: (libc)Consistency Checking.
* atan2f: (libc)Inverse Trig Functions.
* atan2: (libc)Inverse Trig Functions.
* atan2l: (libc)Inverse Trig Functions.
* atanf: (libc)Inverse Trig Functions.
* atanhf: (libc)Hyperbolic Functions.
* atanh: (libc)Hyperbolic Functions.
* atanhl: (libc)Hyperbolic Functions.
* atan: (libc)Inverse Trig 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_fd: (libc)Backtraces.
* backtrace_symbols: (libc)Backtraces.
* basename: (libc)Finding Tokens in a String.
* basename: (libc)Finding Tokens in a String.
* BC_BASE_MAX: (libc)Utility Limits.
* BC_DIM_MAX: (libc)Utility Limits.
* bcmp: (libc)String/Array Comparison.
* bcopy: (libc)Copying Strings and Arrays.
* BC_SCALE_MAX: (libc)Utility Limits.
* BC_STRING_MAX: (libc)Utility Limits.
* bind: (libc)Setting Address.
* bind_textdomain_codeset: (libc)Charset conversion in gettext.
* bindtextdomain: (libc)Locating gettext catalog.
* BRKINT: (libc)Input Modes.
* brk: (libc)Resizing the Data Segment.
* bsearch: (libc)Array Search Function.
* btowc: (libc)Converting a Character.
* BUFSIZ: (libc)Controlling Buffering.
* bzero: (libc)Copying Strings and Arrays.
* cabsf: (libc)Absolute Value.
* cabs: (libc)Absolute Value.
* cabsl: (libc)Absolute Value.
* cacosf: (libc)Inverse Trig Functions.
* cacoshf: (libc)Hyperbolic Functions.
* cacosh: (libc)Hyperbolic Functions.
* cacoshl: (libc)Hyperbolic Functions.
* cacos: (libc)Inverse Trig Functions.
* cacosl: (libc)Inverse Trig Functions.
* calloc: (libc)Allocating Cleared Space.
* canonicalize_file_name: (libc)Symbolic Links.
* canonicalizef: (libc)FP Bit Twiddling.
* canonicalize: (libc)FP Bit Twiddling.
* canonicalizel: (libc)FP Bit Twiddling.
* cargf: (libc)Operations on Complex.
* carg: (libc)Operations on Complex.
* cargl: (libc)Operations on Complex.
* casinf: (libc)Inverse Trig Functions.
* casinhf: (libc)Hyperbolic Functions.
* casinh: (libc)Hyperbolic Functions.
* casinhl: (libc)Hyperbolic Functions.
* casin: (libc)Inverse Trig Functions.
* casinl: (libc)Inverse Trig Functions.
* catanf: (libc)Inverse Trig Functions.
* catanhf: (libc)Hyperbolic Functions.
* catanh: (libc)Hyperbolic Functions.
* catanhl: (libc)Hyperbolic Functions.
* catan: (libc)Inverse Trig 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.
* cbrtf: (libc)Exponents and Logarithms.
* cbrt: (libc)Exponents and Logarithms.
* cbrtl: (libc)Exponents and Logarithms.
* ccosf: (libc)Trig Functions.
* ccoshf: (libc)Hyperbolic Functions.
* ccosh: (libc)Hyperbolic Functions.
* ccoshl: (libc)Hyperbolic Functions.
* ccos: (libc)Trig Functions.
* ccosl: (libc)Trig Functions.
* CCTS_OFLOW: (libc)Control Modes.
* ceilf: (libc)Rounding Functions.
* ceil: (libc)Rounding Functions.
* ceill: (libc)Rounding Functions.
* cexpf: (libc)Exponents and Logarithms.
* cexp: (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.
* CHILD_MAX: (libc)General Limits.
* chmod: (libc)Setting Permissions.
* chown: (libc)File Owner.
* CIGNORE: (libc)Control Modes.
* cimagf: (libc)Operations on Complex.
* cimag: (libc)Operations on Complex.
* cimagl: (libc)Operations on Complex.
* clearenv: (libc)Environment Access.
* clearerr: (libc)Error Recovery.
* clearerr_unlocked: (libc)Error Recovery.
* CLK_TCK: (libc)Processor Time.
* CLOCAL: (libc)Control Modes.
* clock: (libc)CPU Time.
* CLOCKS_PER_SEC: (libc)CPU Time.
* clog10f: (libc)Exponents and Logarithms.
* clog10: (libc)Exponents and Logarithms.
* clog10l: (libc)Exponents and Logarithms.
* clogf: (libc)Exponents and Logarithms.
* clog: (libc)Exponents and Logarithms.
* clogl: (libc)Exponents and Logarithms.
* closedir: (libc)Reading/Closing Directory.
* close: (libc)Opening and Closing Files.
* closelog: (libc)closelog.
* COLL_WEIGHTS_MAX: (libc)Utility Limits.
* _Complex_I: (libc)Complex Numbers.
* confstr: (libc)String Parameters.
* conjf: (libc)Operations on Complex.
* conj: (libc)Operations on Complex.
* conjl: (libc)Operations on Complex.
* connect: (libc)Connecting.
* copysignf: (libc)FP Bit Twiddling.
* copysign: (libc)FP Bit Twiddling.
* copysignl: (libc)FP Bit Twiddling.
* cosf: (libc)Trig Functions.
* coshf: (libc)Hyperbolic Functions.
* cosh: (libc)Hyperbolic Functions.
* coshl: (libc)Hyperbolic Functions.
* cos: (libc)Trig Functions.
* cosl: (libc)Trig Functions.
* cpowf: (libc)Exponents and Logarithms.
* cpow: (libc)Exponents and Logarithms.
* cpowl: (libc)Exponents and Logarithms.
* cprojf: (libc)Operations on Complex.
* cproj: (libc)Operations on Complex.
* cprojl: (libc)Operations on Complex.
* 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.
* crealf: (libc)Operations on Complex.
* creal: (libc)Operations on Complex.
* creall: (libc)Operations on Complex.
* creat64: (libc)Opening and Closing Files.
* creat: (libc)Opening and Closing Files.
* CRTS_IFLOW: (libc)Control Modes.
* crypt: (libc)crypt.
* crypt_r: (libc)crypt.
* CS5: (libc)Control Modes.
* CS6: (libc)Control Modes.
* CS7: (libc)Control Modes.
* CS8: (libc)Control Modes.
* csinf: (libc)Trig Functions.
* csinhf: (libc)Hyperbolic Functions.
* csinh: (libc)Hyperbolic Functions.
* csinhl: (libc)Hyperbolic Functions.
* csin: (libc)Trig Functions.
* csinl: (libc)Trig Functions.
* CSIZE: (libc)Control Modes.
* csqrtf: (libc)Exponents and Logarithms.
* csqrt: (libc)Exponents and Logarithms.
* csqrtl: (libc)Exponents and Logarithms.
* CSTOPB: (libc)Control Modes.
* ctanf: (libc)Trig Functions.
* ctanhf: (libc)Hyperbolic Functions.
* ctanh: (libc)Hyperbolic Functions.
* ctanhl: (libc)Hyperbolic Functions.
* ctan: (libc)Trig 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_FAILED: (libc)DES Encryption.
* 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.
* dremf: (libc)Remainder Functions.
* drem: (libc)Remainder Functions.
* dreml: (libc)Remainder Functions.
* DTTOIF: (libc)Directory Entries.
* dup2: (libc)Duplicating Descriptors.
* dup: (libc)Duplicating Descriptors.
* 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.
* EBADFD: (libc)Error Codes.
* EBADF: (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.
* ecb_crypt: (libc)DES Encryption.
* ECHILD: (libc)Error Codes.
* ECHOCTL: (libc)Local Modes.
* ECHOE: (libc)Local Modes.
* ECHOKE: (libc)Local Modes.
* ECHOK: (libc)Local Modes.
* ECHO: (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.
* ecvt: (libc)System V Number Conversion.
* ecvt_r: (libc)System V Number Conversion.
* EDEADLK: (libc)Error Codes.
* EDEADLOCK: (libc)Error Codes.
* EDESTADDRREQ: (libc)Error Codes.
* EDIED: (libc)Error Codes.
* ED: (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.
* EHWPOISON: (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.
* EKEYEXPIRED: (libc)Error Codes.
* EKEYREJECTED: (libc)Error Codes.
* EKEYREVOKED: (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.
* 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.
* 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.
* ENOKEY: (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.
* ENOTRECOVERABLE: (libc)Error Codes.
* ENOTSOCK: (libc)Error Codes.
* ENOTSUP: (libc)Error Codes.
* ENOTTY: (libc)Error Codes.
* ENOTUNIQ: (libc)Error Codes.
* envz_add: (libc)Envz Functions.
* envz_entry: (libc)Envz Functions.
* envz_get: (libc)Envz Functions.
* envz_merge: (libc)Envz Functions.
* envz_remove: (libc)Envz Functions.
* envz_strip: (libc)Envz Functions.
* ENXIO: (libc)Error Codes.
* EOF: (libc)EOF and Errors.
* EOPNOTSUPP: (libc)Error Codes.
* EOVERFLOW: (libc)Error Codes.
* EOWNERDEAD: (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.
* erand48: (libc)SVID Random.
* erand48_r: (libc)SVID Random.
* ERANGE: (libc)Error Codes.
* EREMCHG: (libc)Error Codes.
* EREMOTEIO: (libc)Error Codes.
* EREMOTE: (libc)Error Codes.
* ERESTART: (libc)Error Codes.
* erfcf: (libc)Special Functions.
* erfc: (libc)Special Functions.
* erfcl: (libc)Special Functions.
* erff: (libc)Special Functions.
* ERFKILL: (libc)Error Codes.
* erf: (libc)Special Functions.
* erfl: (libc)Special Functions.
* EROFS: (libc)Error Codes.
* ERPCMISMATCH: (libc)Error Codes.
* err: (libc)Error Messages.
* errno: (libc)Checking for Errors.
* error_at_line: (libc)Error Messages.
* error: (libc)Error Messages.
* errx: (libc)Error Messages.
* 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.
* ETIMEDOUT: (libc)Error Codes.
* ETIME: (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.
* execle: (libc)Executing a File.
* execl: (libc)Executing a File.
* execlp: (libc)Executing a File.
* execve: (libc)Executing a File.
* execv: (libc)Executing a File.
* execvp: (libc)Executing a File.
* EXFULL: (libc)Error Codes.
* EXIT_FAILURE: (libc)Exit Status.
* exit: (libc)Normal Termination.
* _exit: (libc)Termination Internals.
* _Exit: (libc)Termination Internals.
* EXIT_SUCCESS: (libc)Exit Status.
* exp10f: (libc)Exponents and Logarithms.
* exp10: (libc)Exponents and Logarithms.
* exp10l: (libc)Exponents and Logarithms.
* exp2f: (libc)Exponents and Logarithms.
* exp2: (libc)Exponents and Logarithms.
* exp2l: (libc)Exponents and Logarithms.
* expf: (libc)Exponents and Logarithms.
* exp: (libc)Exponents and Logarithms.
* explicit_bzero: (libc)Erasing Sensitive Data.
* expl: (libc)Exponents and Logarithms.
* expm1f: (libc)Exponents and Logarithms.
* expm1: (libc)Exponents and Logarithms.
* expm1l: (libc)Exponents and Logarithms.
* EXPR_NEST_MAX: (libc)Utility Limits.
* fabsf: (libc)Absolute Value.
* fabs: (libc)Absolute Value.
* fabsl: (libc)Absolute Value.
* __fbufsize: (libc)Controlling Buffering.
* fchdir: (libc)Working Directory.
* fchmod: (libc)Setting Permissions.
* fchown: (libc)File Owner.
* fcloseall: (libc)Closing Streams.
* fclose: (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.
* FD_CLOEXEC: (libc)Descriptor Flags.
* FD_CLR: (libc)Waiting for I/O.
* fdimf: (libc)Misc FP Arithmetic.
* fdim: (libc)Misc FP Arithmetic.
* fdiml: (libc)Misc FP Arithmetic.
* FD_ISSET: (libc)Waiting for I/O.
* fdopendir: (libc)Opening a Directory.
* fdopen: (libc)Descriptors and Streams.
* FD_SET: (libc)Waiting for I/O.
* FD_SETSIZE: (libc)Waiting for I/O.
* F_DUPFD: (libc)Duplicating Descriptors.
* FD_ZERO: (libc)Waiting for I/O.
* feclearexcept: (libc)Status bit operations.
* fedisableexcept: (libc)Control Functions.
* feenableexcept: (libc)Control Functions.
* fegetenv: (libc)Control Functions.
* fegetexceptflag: (libc)Status bit operations.
* fegetexcept: (libc)Control Functions.
* fegetmode: (libc)Control Functions.
* 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.
* fesetexcept: (libc)Status bit operations.
* fesetmode: (libc)Control Functions.
* fesetround: (libc)Rounding.
* FE_SNANS_ALWAYS_SIGNAL: (libc)Infinity and NaN.
* fetestexceptflag: (libc)Status bit operations.
* 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.
* F_GETFD: (libc)Descriptor Flags.
* F_GETFL: (libc)Getting File Status Flags.
* fgetgrent: (libc)Scanning All Groups.
* fgetgrent_r: (libc)Scanning All Groups.
* F_GETLK: (libc)File Locks.
* F_GETOWN: (libc)Interrupt Input.
* 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.
* FILENAME_MAX: (libc)Limits for Files.
* fileno: (libc)Descriptors and Streams.
* fileno_unlocked: (libc)Descriptors and Streams.
* finitef: (libc)Floating Point Classes.
* finite: (libc)Floating Point Classes.
* finitel: (libc)Floating Point Classes.
* __flbf: (libc)Controlling Buffering.
* flockfile: (libc)Streams and Threads.
* floorf: (libc)Rounding Functions.
* floor: (libc)Rounding Functions.
* floorl: (libc)Rounding Functions.
* _flushlbf: (libc)Flushing Buffers.
* FLUSHO: (libc)Local Modes.
* fmaf: (libc)Misc FP Arithmetic.
* fma: (libc)Misc FP Arithmetic.
* fmal: (libc)Misc FP Arithmetic.
* fmaxf: (libc)Misc FP Arithmetic.
* fmax: (libc)Misc FP Arithmetic.
* fmaxl: (libc)Misc FP Arithmetic.
* fmaxmagf: (libc)Misc FP Arithmetic.
* fmaxmag: (libc)Misc FP Arithmetic.
* fmaxmagl: (libc)Misc FP Arithmetic.
* fmemopen: (libc)String Streams.
* fminf: (libc)Misc FP Arithmetic.
* fmin: (libc)Misc FP Arithmetic.
* fminl: (libc)Misc FP Arithmetic.
* fminmagf: (libc)Misc FP Arithmetic.
* fminmag: (libc)Misc FP Arithmetic.
* fminmagl: (libc)Misc FP Arithmetic.
* fmodf: (libc)Remainder Functions.
* fmod: (libc)Remainder Functions.
* fmodl: (libc)Remainder Functions.
* fmtmsg: (libc)Printing Formatted Messages.
* fnmatch: (libc)Wildcard Matching.
* F_OFD_GETLK: (libc)Open File Description Locks.
* F_OFD_SETLK: (libc)Open File Description Locks.
* F_OFD_SETLKW: (libc)Open File Description Locks.
* F_OK: (libc)Testing File Access.
* fopen64: (libc)Opening Streams.
* fopencookie: (libc)Streams and Cookies.
* fopen: (libc)Opening Streams.
* FOPEN_MAX: (libc)Opening Streams.
* fork: (libc)Creating a Process.
* forkpty: (libc)Pseudo-Terminal Pairs.
* fpathconf: (libc)Pathconf.
* fpclassify: (libc)Floating Point Classes.
* __fpending: (libc)Controlling Buffering.
* FP_ILOGB0: (libc)Exponents and Logarithms.
* FP_ILOGBNAN: (libc)Exponents and Logarithms.
* FP_LLOGB0: (libc)Exponents and Logarithms.
* FP_LLOGBNAN: (libc)Exponents and Logarithms.
* fprintf: (libc)Formatted Output Functions.
* __fpurge: (libc)Flushing Buffers.
* 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.
* __freadable: (libc)Opening Streams.
* __freading: (libc)Opening Streams.
* fread: (libc)Block Input/Output.
* fread_unlocked: (libc)Block Input/Output.
* free: (libc)Freeing after Malloc.
* freopen64: (libc)Opening Streams.
* freopen: (libc)Opening Streams.
* frexpf: (libc)Normalization Functions.
* frexp: (libc)Normalization Functions.
* frexpl: (libc)Normalization Functions.
* fromfpf: (libc)Rounding Functions.
* fromfp: (libc)Rounding Functions.
* fromfpl: (libc)Rounding Functions.
* fromfpxf: (libc)Rounding Functions.
* fromfpx: (libc)Rounding Functions.
* fromfpxl: (libc)Rounding Functions.
* fscanf: (libc)Formatted Input Functions.
* fseek: (libc)File Positioning.
* fseeko64: (libc)File Positioning.
* fseeko: (libc)File Positioning.
* F_SETFD: (libc)Descriptor Flags.
* F_SETFL: (libc)Getting File Status Flags.
* F_SETLK: (libc)File Locks.
* F_SETLKW: (libc)File Locks.
* __fsetlocking: (libc)Streams and Threads.
* F_SETOWN: (libc)Interrupt Input.
* 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.
* __fwritable: (libc)Opening Streams.
* fwrite: (libc)Block Input/Output.
* fwrite_unlocked: (libc)Block Input/Output.
* __fwriting: (libc)Opening Streams.
* fwscanf: (libc)Formatted Input Functions.
* gammaf: (libc)Special Functions.
* gamma: (libc)Special Functions.
* gammal: (libc)Special Functions.
* __gconv_end_fct: (libc)glibc iconv Implementation.
* __gconv_fct: (libc)glibc iconv Implementation.
* __gconv_init_fct: (libc)glibc iconv Implementation.
* gcvt: (libc)System V Number Conversion.
* getauxval: (libc)Auxiliary Vector.
* get_avphys_pages: (libc)Query Memory Parameters.
* getchar: (libc)Character Input.
* getchar_unlocked: (libc)Character Input.
* getc: (libc)Character Input.
* getcontext: (libc)System V contexts.
* getc_unlocked: (libc)Character Input.
* get_current_dir_name: (libc)Working Directory.
* 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.
* getentropy: (libc)Unpredictable Bytes.
* 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.
* get_nprocs_conf: (libc)Processor Resources.
* get_nprocs: (libc)Processor Resources.
* 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.
* getpayloadf: (libc)FP Bit Twiddling.
* getpayload: (libc)FP Bit Twiddling.
* getpayloadl: (libc)FP Bit Twiddling.
* getpeername: (libc)Who is Connected.
* getpgid: (libc)Process Group Functions.
* getpgrp: (libc)Process Group Functions.
* get_phys_pages: (libc)Query Memory Parameters.
* 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.
* getrandom: (libc)Unpredictable Bytes.
* getrlimit64: (libc)Limits on Resources.
* getrlimit: (libc)Limits on Resources.
* getrusage: (libc)Resource Usage.
* getservbyname: (libc)Services Database.
* getservbyport: (libc)Services Database.
* getservent: (libc)Services Database.
* getsid: (libc)Process Group Functions.
* gets: (libc)Line Input.
* 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.
* getwchar: (libc)Character Input.
* getwchar_unlocked: (libc)Character Input.
* getwc: (libc)Character Input.
* getwc_unlocked: (libc)Character Input.
* getwd: (libc)Working Directory.
* getw: (libc)Character Input.
* glob64: (libc)Calling Glob.
* globfree64: (libc)More Flags for Globbing.
* globfree: (libc)More Flags for Globbing.
* glob: (libc)Calling Glob.
* 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.
* HUGE_VALF: (libc)Math Error Reporting.
* HUGE_VAL: (libc)Math Error Reporting.
* HUGE_VALL: (libc)Math Error Reporting.
* HUPCL: (libc)Control Modes.
* hypotf: (libc)Exponents and Logarithms.
* hypot: (libc)Exponents and Logarithms.
* hypotl: (libc)Exponents and Logarithms.
* ICANON: (libc)Local Modes.
* iconv_close: (libc)Generic Conversion Interface.
* iconv: (libc)Generic Conversion Interface.
* iconv_open: (libc)Generic Conversion Interface.
* ICRNL: (libc)Input Modes.
* IEXTEN: (libc)Local Modes.
* if_freenameindex: (libc)Interface Naming.
* if_indextoname: (libc)Interface Naming.
* if_nameindex: (libc)Interface Naming.
* if_nametoindex: (libc)Interface Naming.
* IFNAMSIZ: (libc)Interface Naming.
* IFTODT: (libc)Directory Entries.
* IGNBRK: (libc)Input Modes.
* IGNCR: (libc)Input Modes.
* IGNPAR: (libc)Input Modes.
* I: (libc)Complex Numbers.
* ilogbf: (libc)Exponents and Logarithms.
* ilogb: (libc)Exponents and Logarithms.
* ilogbl: (libc)Exponents and Logarithms.
* _Imaginary_I: (libc)Complex Numbers.
* imaxabs: (libc)Absolute Value.
* IMAXBEL: (libc)Input Modes.
* imaxdiv: (libc)Integer Division.
* in6addr_any: (libc)Host Address Data Type.
* in6addr_loopback: (libc)Host Address Data Type.
* 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.
* 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.
* INFINITY: (libc)Infinity and NaN.
* initgroups: (libc)Setting Groups.
* initstate: (libc)BSD Random.
* initstate_r: (libc)BSD Random.
* INLCR: (libc)Input Modes.
* innetgr: (libc)Netgroup Membership.
* INPCK: (libc)Input Modes.
* ioctl: (libc)IOCTLs.
* _IOFBF: (libc)Controlling Buffering.
* _IOLBF: (libc)Controlling Buffering.
* _IONBF: (libc)Controlling Buffering.
* IPPORT_RESERVED: (libc)Ports.
* IPPORT_USERRESERVED: (libc)Ports.
* 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.
* iscanonical: (libc)Floating Point Classes.
* iscntrl: (libc)Classification of Characters.
* isdigit: (libc)Classification of Characters.
* iseqsig: (libc)FP Comparison Functions.
* isfinite: (libc)Floating Point Classes.
* isgraph: (libc)Classification of Characters.
* isgreaterequal: (libc)FP Comparison Functions.
* isgreater: (libc)FP Comparison Functions.
* ISIG: (libc)Local Modes.
* isinff: (libc)Floating Point Classes.
* isinf: (libc)Floating Point Classes.
* isinfl: (libc)Floating Point Classes.
* islessequal: (libc)FP Comparison Functions.
* islessgreater: (libc)FP Comparison Functions.
* isless: (libc)FP Comparison Functions.
* islower: (libc)Classification of Characters.
* isnanf: (libc)Floating Point Classes.
* isnan: (libc)Floating Point Classes.
* isnan: (libc)Floating Point Classes.
* isnanl: (libc)Floating Point Classes.
* isnormal: (libc)Floating Point Classes.
* isprint: (libc)Classification of Characters.
* ispunct: (libc)Classification of Characters.
* issignaling: (libc)Floating Point Classes.
* isspace: (libc)Classification of Characters.
* issubnormal: (libc)Floating Point Classes.
* ISTRIP: (libc)Input Modes.
* 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.
* iszero: (libc)Floating Point Classes.
* IXANY: (libc)Input Modes.
* IXOFF: (libc)Input Modes.
* IXON: (libc)Input Modes.
* j0f: (libc)Special Functions.
* j0: (libc)Special Functions.
* j0l: (libc)Special Functions.
* j1f: (libc)Special Functions.
* j1: (libc)Special Functions.
* j1l: (libc)Special Functions.
* jnf: (libc)Special Functions.
* jn: (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.
* L_ctermid: (libc)Identifying the Terminal.
* L_cuserid: (libc)Who Logged In.
* ldexpf: (libc)Normalization Functions.
* ldexp: (libc)Normalization Functions.
* ldexpl: (libc)Normalization Functions.
* ldiv: (libc)Integer Division.
* lfind: (libc)Array Search Function.
* lgammaf: (libc)Special Functions.
* lgammaf_r: (libc)Special Functions.
* lgamma: (libc)Special Functions.
* lgammal: (libc)Special Functions.
* lgammal_r: (libc)Special Functions.
* lgamma_r: (libc)Special Functions.
* LINE_MAX: (libc)Utility Limits.
* link: (libc)Hard Links.
* LINK_MAX: (libc)Limits for Files.
* lio_listio64: (libc)Asynchronous Reads/Writes.
* lio_listio: (libc)Asynchronous Reads/Writes.
* listen: (libc)Listening.
* llabs: (libc)Absolute Value.
* lldiv: (libc)Integer Division.
* llogbf: (libc)Exponents and Logarithms.
* llogb: (libc)Exponents and Logarithms.
* llogbl: (libc)Exponents and Logarithms.
* llrintf: (libc)Rounding Functions.
* llrint: (libc)Rounding Functions.
* llrintl: (libc)Rounding Functions.
* llroundf: (libc)Rounding Functions.
* llround: (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.
* log10f: (libc)Exponents and Logarithms.
* log10: (libc)Exponents and Logarithms.
* log10l: (libc)Exponents and Logarithms.
* log1pf: (libc)Exponents and Logarithms.
* log1p: (libc)Exponents and Logarithms.
* log1pl: (libc)Exponents and Logarithms.
* log2f: (libc)Exponents and Logarithms.
* log2: (libc)Exponents and Logarithms.
* log2l: (libc)Exponents and Logarithms.
* logbf: (libc)Exponents and Logarithms.
* logb: (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.
* log: (libc)Exponents and Logarithms.
* 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.
* lrintf: (libc)Rounding Functions.
* lrint: (libc)Rounding Functions.
* lrintl: (libc)Rounding Functions.
* lroundf: (libc)Rounding Functions.
* lround: (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.
* L_tmpnam: (libc)Temporary Files.
* 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.
* MAX_CANON: (libc)Limits for Files.
* MAX_INPUT: (libc)Limits for Files.
* MAXNAMLEN: (libc)Limits for Files.
* MAXSYMLINKS: (libc)Symbolic Links.
* MB_CUR_MAX: (libc)Selecting the Conversion.
* mblen: (libc)Non-reentrant Character Conversion.
* MB_LEN_MAX: (libc)Selecting the 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.
* MDMBUF: (libc)Control Modes.
* memalign: (libc)Aligned Memory Blocks.
* memccpy: (libc)Copying Strings and Arrays.
* memchr: (libc)Search Functions.
* memcmp: (libc)String/Array Comparison.
* memcpy: (libc)Copying Strings and Arrays.
* memfrob: (libc)Trivial Encryption.
* memmem: (libc)Search Functions.
* memmove: (libc)Copying Strings and Arrays.
* mempcpy: (libc)Copying Strings and Arrays.
* memrchr: (libc)Search Functions.
* memset: (libc)Copying Strings and Arrays.
* 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.
* mlockall: (libc)Page Lock Functions.
* mlock: (libc)Page Lock Functions.
* mmap64: (libc)Memory-mapped I/O.
* mmap: (libc)Memory-mapped I/O.
* modff: (libc)Rounding Functions.
* modf: (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.
* MSG_DONTROUTE: (libc)Socket Data Options.
* MSG_OOB: (libc)Socket Data Options.
* MSG_PEEK: (libc)Socket Data Options.
* msync: (libc)Memory-mapped I/O.
* mtrace: (libc)Tracing malloc.
* munlockall: (libc)Page Lock Functions.
* munlock: (libc)Page Lock Functions.
* munmap: (libc)Memory-mapped I/O.
* muntrace: (libc)Tracing malloc.
* NAME_MAX: (libc)Limits for Files.
* nanf: (libc)FP Bit Twiddling.
* nan: (libc)FP Bit Twiddling.
* NAN: (libc)Infinity and NaN.
* nanl: (libc)FP Bit Twiddling.
* nanosleep: (libc)Sleeping.
* NCCS: (libc)Mode Data Types.
* nearbyintf: (libc)Rounding Functions.
* nearbyint: (libc)Rounding Functions.
* nearbyintl: (libc)Rounding Functions.
* nextafterf: (libc)FP Bit Twiddling.
* nextafter: (libc)FP Bit Twiddling.
* nextafterl: (libc)FP Bit Twiddling.
* nextdownf: (libc)FP Bit Twiddling.
* nextdown: (libc)FP Bit Twiddling.
* nextdownl: (libc)FP Bit Twiddling.
* nexttowardf: (libc)FP Bit Twiddling.
* nexttoward: (libc)FP Bit Twiddling.
* nexttowardl: (libc)FP Bit Twiddling.
* nextupf: (libc)FP Bit Twiddling.
* nextup: (libc)FP Bit Twiddling.
* nextupl: (libc)FP Bit Twiddling.
* nftw64: (libc)Working with Directory Trees.
* nftw: (libc)Working with Directory Trees.
* ngettext: (libc)Advanced gettext functions.
* NGROUPS_MAX: (libc)General Limits.
* nice: (libc)Traditional Scheduling Functions.
* nl_langinfo: (libc)The Elegant and Fast Way.
* NOFLSH: (libc)Local Modes.
* NOKERNINFO: (libc)Local Modes.
* nrand48: (libc)SVID Random.
* nrand48_r: (libc)SVID Random.
* NSIG: (libc)Standard Signals.
* ntohl: (libc)Byte Order.
* ntohs: (libc)Byte Order.
* ntp_adjtime: (libc)High Accuracy Clock.
* ntp_gettime: (libc)High Accuracy Clock.
* NULL: (libc)Null Pointer Constant.
* O_ACCMODE: (libc)Access Modes.
* O_APPEND: (libc)Operating Modes.
* O_ASYNC: (libc)Operating Modes.
* obstack_1grow_fast: (libc)Extra Fast Growing.
* obstack_1grow: (libc)Growing Objects.
* obstack_alignment_mask: (libc)Obstacks Data Alignment.
* obstack_alloc: (libc)Allocation in an Obstack.
* obstack_base: (libc)Status of an Obstack.
* obstack_blank_fast: (libc)Extra Fast Growing.
* obstack_blank: (libc)Growing Objects.
* 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_fast: (libc)Extra Fast Growing.
* obstack_int_grow: (libc)Growing Objects.
* 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_fast: (libc)Extra Fast Growing.
* obstack_ptr_grow: (libc)Growing Objects.
* obstack_room: (libc)Extra Fast Growing.
* obstack_vprintf: (libc)Variable Arguments Output.
* O_CREAT: (libc)Open-time Flags.
* O_EXCL: (libc)Open-time Flags.
* O_EXEC: (libc)Access Modes.
* O_EXLOCK: (libc)Open-time Flags.
* offsetof: (libc)Structure Measurement.
* O_FSYNC: (libc)Operating Modes.
* O_IGNORE_CTTY: (libc)Open-time Flags.
* O_NDELAY: (libc)Operating Modes.
* on_exit: (libc)Cleanups on Exit.
* ONLCR: (libc)Output Modes.
* O_NOATIME: (libc)Operating Modes.
* O_NOCTTY: (libc)Open-time Flags.
* ONOEOT: (libc)Output Modes.
* O_NOLINK: (libc)Open-time Flags.
* O_NONBLOCK: (libc)Open-time Flags.
* O_NONBLOCK: (libc)Operating Modes.
* O_NOTRANS: (libc)Open-time Flags.
* open64: (libc)Opening and Closing Files.
* opendir: (libc)Opening a Directory.
* open: (libc)Opening and Closing Files.
* openlog: (libc)openlog.
* OPEN_MAX: (libc)General Limits.
* open_memstream: (libc)String Streams.
* openpty: (libc)Pseudo-Terminal Pairs.
* OPOST: (libc)Output Modes.
* 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.
* OXTABS: (libc)Output Modes.
* PA_FLAG_MASK: (libc)Parsing a Template String.
* PARENB: (libc)Control Modes.
* PARMRK: (libc)Input Modes.
* PARODD: (libc)Control Modes.
* parse_printf_format: (libc)Parsing a Template String.
* pathconf: (libc)Pathconf.
* PATH_MAX: (libc)Limits for Files.
* _PATH_UTMP: (libc)Manipulating the Database.
* _PATH_WTMP: (libc)Manipulating the Database.
* pause: (libc)Using Pause.
* pclose: (libc)Pipe to a Subprocess.
* PENDIN: (libc)Local Modes.
* perror: (libc)Error Messages.
* 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.
* pipe: (libc)Creating a Pipe.
* popen: (libc)Pipe to a Subprocess.
* _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_fallocate64: (libc)Storage Allocation.
* posix_fallocate: (libc)Storage Allocation.
* _POSIX_JOB_CONTROL: (libc)System Options.
* posix_memalign: (libc)Aligned Memory Blocks.
* _POSIX_NO_TRUNC: (libc)Options for Files.
* _POSIX_SAVED_IDS: (libc)System Options.
* _POSIX_VDISABLE: (libc)Options for Files.
* _POSIX_VERSION: (libc)Version Supported.
* pow10f: (libc)Exponents and Logarithms.
* pow10: (libc)Exponents and Logarithms.
* pow10l: (libc)Exponents and Logarithms.
* powf: (libc)Exponents and Logarithms.
* pow: (libc)Exponents and Logarithms.
* powl: (libc)Exponents and Logarithms.
* __ppc_get_timebase_freq: (libc)PowerPC.
* __ppc_get_timebase: (libc)PowerPC.
* __ppc_mdoio: (libc)PowerPC.
* __ppc_mdoom: (libc)PowerPC.
* __ppc_set_ppr_low: (libc)PowerPC.
* __ppc_set_ppr_med_high: (libc)PowerPC.
* __ppc_set_ppr_med: (libc)PowerPC.
* __ppc_set_ppr_med_low: (libc)PowerPC.
* __ppc_set_ppr_very_low: (libc)PowerPC.
* __ppc_yield: (libc)PowerPC.
* pread64: (libc)I/O Primitives.
* pread: (libc)I/O Primitives.
* printf: (libc)Formatted Output Functions.
* printf_size_info: (libc)Predefined Printf Handlers.
* printf_size: (libc)Predefined Printf Handlers.
* psignal: (libc)Signal Messages.
* pthread_getattr_default_np: (libc)Default Thread Attributes.
* pthread_getspecific: (libc)Thread-specific Data.
* pthread_key_create: (libc)Thread-specific Data.
* pthread_key_delete: (libc)Thread-specific Data.
* pthread_setattr_default_np: (libc)Default Thread Attributes.
* pthread_setspecific: (libc)Thread-specific Data.
* P_tmpdir: (libc)Temporary Files.
* ptsname: (libc)Allocation.
* ptsname_r: (libc)Allocation.
* putchar: (libc)Simple Output.
* putchar_unlocked: (libc)Simple Output.
* putc: (libc)Simple Output.
* putc_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.
* putwchar: (libc)Simple Output.
* putwchar_unlocked: (libc)Simple Output.
* putwc: (libc)Simple Output.
* putwc_unlocked: (libc)Simple Output.
* putw: (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_MAX: (libc)ISO Random.
* random: (libc)BSD Random.
* random_r: (libc)BSD Random.
* rand_r: (libc)ISO Random.
* rawmemchr: (libc)Search Functions.
* readdir64: (libc)Reading/Closing Directory.
* readdir64_r: (libc)Reading/Closing Directory.
* readdir: (libc)Reading/Closing Directory.
* readdir_r: (libc)Reading/Closing Directory.
* read: (libc)I/O Primitives.
* readlink: (libc)Symbolic Links.
* readv: (libc)Scatter-Gather.
* realloc: (libc)Changing Block Size.
* realpath: (libc)Symbolic Links.
* recvfrom: (libc)Receiving Datagrams.
* recv: (libc)Receiving Data.
* recvmsg: (libc)Receiving Datagrams.
* RE_DUP_MAX: (libc)General Limits.
* 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.
* remainderf: (libc)Remainder Functions.
* remainder: (libc)Remainder Functions.
* remainderl: (libc)Remainder Functions.
* remove: (libc)Deleting Files.
* rename: (libc)Renaming Files.
* rewinddir: (libc)Random Access Directory.
* rewind: (libc)File Positioning.
* rindex: (libc)Search Functions.
* rintf: (libc)Rounding Functions.
* rint: (libc)Rounding Functions.
* rintl: (libc)Rounding Functions.
* RLIM_INFINITY: (libc)Limits on Resources.
* rmdir: (libc)Deleting Files.
* R_OK: (libc)Testing File Access.
* roundevenf: (libc)Rounding Functions.
* roundeven: (libc)Rounding Functions.
* roundevenl: (libc)Rounding Functions.
* roundf: (libc)Rounding Functions.
* round: (libc)Rounding Functions.
* roundl: (libc)Rounding Functions.
* rpmatch: (libc)Yes-or-No Questions.
* SA_NOCLDSTOP: (libc)Flags for Sigaction.
* SA_ONSTACK: (libc)Flags for Sigaction.
* SA_RESTART: (libc)Flags for Sigaction.
* sbrk: (libc)Resizing the Data Segment.
* scalbf: (libc)Normalization Functions.
* scalb: (libc)Normalization Functions.
* scalbl: (libc)Normalization Functions.
* scalblnf: (libc)Normalization Functions.
* scalbln: (libc)Normalization Functions.
* scalblnl: (libc)Normalization Functions.
* scalbnf: (libc)Normalization Functions.
* scalbn: (libc)Normalization Functions.
* scalbnl: (libc)Normalization Functions.
* scandir64: (libc)Scanning Directory Content.
* scandir: (libc)Scanning Directory Content.
* scanf: (libc)Formatted Input Functions.
* sched_getaffinity: (libc)CPU Affinity.
* sched_getparam: (libc)Basic Scheduling Functions.
* sched_get_priority_max: (libc)Basic Scheduling Functions.
* sched_get_priority_min: (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.
* secure_getenv: (libc)Environment Access.
* seed48: (libc)SVID Random.
* seed48_r: (libc)SVID Random.
* SEEK_CUR: (libc)File Positioning.
* seekdir: (libc)Random Access Directory.
* SEEK_END: (libc)File Positioning.
* SEEK_SET: (libc)File Positioning.
* select: (libc)Waiting for I/O.
* sem_close: (libc)Semaphores.
* semctl: (libc)Semaphores.
* sem_destroy: (libc)Semaphores.
* semget: (libc)Semaphores.
* sem_getvalue: (libc)Semaphores.
* sem_init: (libc)Semaphores.
* sem_open: (libc)Semaphores.
* semop: (libc)Semaphores.
* sem_post: (libc)Semaphores.
* semtimedop: (libc)Semaphores.
* sem_timedwait: (libc)Semaphores.
* sem_trywait: (libc)Semaphores.
* sem_unlink: (libc)Semaphores.
* sem_wait: (libc)Semaphores.
* send: (libc)Sending Data.
* sendmsg: (libc)Receiving Datagrams.
* sendto: (libc)Sending Datagrams.
* setbuffer: (libc)Controlling Buffering.
* setbuf: (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.
* setpayloadf: (libc)FP Bit Twiddling.
* setpayload: (libc)FP Bit Twiddling.
* setpayloadl: (libc)FP Bit Twiddling.
* setpayloadsigf: (libc)FP Bit Twiddling.
* setpayloadsig: (libc)FP Bit Twiddling.
* setpayloadsigl: (libc)FP Bit Twiddling.
* 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.
* shm_open: (libc)Memory-mapped I/O.
* shm_unlink: (libc)Memory-mapped I/O.
* shutdown: (libc)Closing a Socket.
* S_IFMT: (libc)Testing File Type.
* SIGABRT: (libc)Program Error Signals.
* sigaction: (libc)Advanced Signal Handling.
* sigaddset: (libc)Signal Sets.
* SIGALRM: (libc)Alarm Signals.
* sigaltstack: (libc)Signal Stack.
* sigblock: (libc)BSD Signal Handling.
* SIGBUS: (libc)Program Error Signals.
* SIGCHLD: (libc)Job Control Signals.
* SIGCLD: (libc)Job Control Signals.
* SIGCONT: (libc)Job Control Signals.
* sigdelset: (libc)Signal Sets.
* sigemptyset: (libc)Signal Sets.
* SIGEMT: (libc)Program Error Signals.
* SIG_ERR: (libc)Basic Signal Handling.
* sigfillset: (libc)Signal Sets.
* SIGFPE: (libc)Program Error Signals.
* SIGHUP: (libc)Termination Signals.
* SIGILL: (libc)Program Error Signals.
* SIGINFO: (libc)Miscellaneous Signals.
* siginterrupt: (libc)BSD Signal Handling.
* SIGINT: (libc)Termination Signals.
* SIGIO: (libc)Asynchronous I/O Signals.
* SIGIOT: (libc)Program Error Signals.
* sigismember: (libc)Signal Sets.
* SIGKILL: (libc)Termination Signals.
* siglongjmp: (libc)Non-Local Exits and Signals.
* SIGLOST: (libc)Operation Error Signals.
* sigmask: (libc)BSD Signal Handling.
* signal: (libc)Basic Signal Handling.
* signbit: (libc)FP Bit Twiddling.
* significandf: (libc)Normalization Functions.
* significand: (libc)Normalization Functions.
* significandl: (libc)Normalization Functions.
* sigpause: (libc)BSD Signal Handling.
* sigpending: (libc)Checking for Pending Signals.
* SIGPIPE: (libc)Operation Error Signals.
* SIGPOLL: (libc)Asynchronous I/O Signals.
* sigprocmask: (libc)Process Signal Mask.
* SIGPROF: (libc)Alarm Signals.
* SIGQUIT: (libc)Termination Signals.
* SIGSEGV: (libc)Program Error Signals.
* sigsetjmp: (libc)Non-Local Exits and Signals.
* sigsetmask: (libc)BSD Signal Handling.
* sigstack: (libc)Signal Stack.
* SIGSTOP: (libc)Job Control Signals.
* sigsuspend: (libc)Sigsuspend.
* 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.
* sincosf: (libc)Trig Functions.
* sincos: (libc)Trig Functions.
* sincosl: (libc)Trig Functions.
* sinf: (libc)Trig Functions.
* sinhf: (libc)Hyperbolic Functions.
* sinh: (libc)Hyperbolic Functions.
* sinhl: (libc)Hyperbolic Functions.
* sin: (libc)Trig Functions.
* sinl: (libc)Trig Functions.
* 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.
* sleep: (libc)Sleeping.
* SNANF: (libc)Infinity and NaN.
* SNAN: (libc)Infinity and NaN.
* SNANL: (libc)Infinity and NaN.
* snprintf: (libc)Formatted Output Functions.
* SOCK_DGRAM: (libc)Communication Styles.
* socket: (libc)Creating a Socket.
* socketpair: (libc)Socket Pairs.
* 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.
* sprintf: (libc)Formatted Output Functions.
* sqrtf: (libc)Exponents and Logarithms.
* sqrt: (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.
* SSIZE_MAX: (libc)General Limits.
* stat64: (libc)Reading Attributes.
* stat: (libc)Reading Attributes.
* stime: (libc)Simple Calendar Time.
* stpcpy: (libc)Copying Strings and Arrays.
* stpncpy: (libc)Truncating Strings.
* strcasecmp: (libc)String/Array Comparison.
* strcasestr: (libc)Search Functions.
* strcat: (libc)Concatenating Strings.
* strchr: (libc)Search Functions.
* strchrnul: (libc)Search Functions.
* strcmp: (libc)String/Array Comparison.
* strcoll: (libc)Collation Functions.
* strcpy: (libc)Copying Strings and Arrays.
* strcspn: (libc)Search Functions.
* strdupa: (libc)Copying Strings and Arrays.
* strdup: (libc)Copying Strings and Arrays.
* STREAM_MAX: (libc)General Limits.
* strerror: (libc)Error Messages.
* strerror_r: (libc)Error Messages.
* strfmon: (libc)Formatting Numbers.
* strfromd: (libc)Printing of Floats.
* strfromf: (libc)Printing of Floats.
* strfroml: (libc)Printing of Floats.
* strfry: (libc)strfry.
* strftime: (libc)Formatting Calendar Time.
* strlen: (libc)String Length.
* strncasecmp: (libc)String/Array Comparison.
* strncat: (libc)Truncating Strings.
* strncmp: (libc)String/Array Comparison.
* strncpy: (libc)Truncating Strings.
* strndupa: (libc)Truncating Strings.
* strndup: (libc)Truncating Strings.
* 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.
* strtold: (libc)Parsing of Floats.
* strtol: (libc)Parsing of Integers.
* 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.
* S_TYPEISMQ: (libc)Testing File Type.
* S_TYPEISSEM: (libc)Testing File Type.
* S_TYPEISSHM: (libc)Testing File Type.
* SUN_LEN: (libc)Local Namespace Details.
* 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.
* tanf: (libc)Trig Functions.
* tanhf: (libc)Hyperbolic Functions.
* tanh: (libc)Hyperbolic Functions.
* tanhl: (libc)Hyperbolic Functions.
* tan: (libc)Trig 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.
* telldir: (libc)Random Access Directory.
* tempnam: (libc)Temporary Files.
* textdomain: (libc)Locating gettext catalog.
* tfind: (libc)Tree Search Function.
* tgammaf: (libc)Special Functions.
* tgamma: (libc)Special Functions.
* tgammal: (libc)Special Functions.
* timegm: (libc)Broken-down Time.
* time: (libc)Simple Calendar Time.
* timelocal: (libc)Broken-down Time.
* times: (libc)Processor Time.
* tmpfile64: (libc)Temporary Files.
* tmpfile: (libc)Temporary Files.
* TMP_MAX: (libc)Temporary Files.
* tmpnam: (libc)Temporary Files.
* tmpnam_r: (libc)Temporary Files.
* toascii: (libc)Case Conversion.
* _tolower: (libc)Case Conversion.
* tolower: (libc)Case Conversion.
* TOSTOP: (libc)Local Modes.
* totalorderf: (libc)FP Comparison Functions.
* totalorder: (libc)FP Comparison Functions.
* totalorderl: (libc)FP Comparison Functions.
* totalordermagf: (libc)FP Comparison Functions.
* totalordermag: (libc)FP Comparison Functions.
* totalordermagl: (libc)FP Comparison Functions.
* _toupper: (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.
* truncate64: (libc)File Size.
* truncate: (libc)File Size.
* truncf: (libc)Rounding Functions.
* trunc: (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.
* TZNAME_MAX: (libc)General Limits.
* tzset: (libc)Time Zone Functions.
* ufromfpf: (libc)Rounding Functions.
* ufromfp: (libc)Rounding Functions.
* ufromfpl: (libc)Rounding Functions.
* ufromfpxf: (libc)Rounding Functions.
* ufromfpx: (libc)Rounding Functions.
* ufromfpxl: (libc)Rounding 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_copy: (libc)Argument Macros.
* va_copy: (libc)Argument Macros.
* va_end: (libc)Argument Macros.
* valloc: (libc)Aligned Memory Blocks.
* vasprintf: (libc)Variable Arguments Output.
* va_start: (libc)Argument Macros.
* VDISCARD: (libc)Other Special.
* VDSUSP: (libc)Signal Characters.
* VEOF: (libc)Editing Characters.
* VEOL2: (libc)Editing Characters.
* VEOL: (libc)Editing Characters.
* VERASE: (libc)Editing Characters.
* 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.
* VINTR: (libc)Signal Characters.
* VKILL: (libc)Editing Characters.
* vlimit: (libc)Limits on Resources.
* VLNEXT: (libc)Other Special.
* VMIN: (libc)Noncanonical Input.
* vprintf: (libc)Variable Arguments Output.
* VQUIT: (libc)Signal Characters.
* VREPRINT: (libc)Editing Characters.
* vscanf: (libc)Variable Arguments Input.
* vsnprintf: (libc)Variable Arguments Output.
* vsprintf: (libc)Variable Arguments Output.
* vsscanf: (libc)Variable Arguments Input.
* VSTART: (libc)Start/Stop Characters.
* VSTATUS: (libc)Other Special.
* VSTOP: (libc)Start/Stop Characters.
* VSUSP: (libc)Signal Characters.
* vswprintf: (libc)Variable Arguments Output.
* vswscanf: (libc)Variable Arguments Input.
* vsyslog: (libc)syslog; vsyslog.
* VTIME: (libc)Noncanonical Input.
* vtimes: (libc)Resource Usage.
* vwarn: (libc)Error Messages.
* vwarnx: (libc)Error Messages.
* VWERASE: (libc)Editing Characters.
* 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.
* WCHAR_MAX: (libc)Extended Char Intro.
* WCHAR_MIN: (libc)Extended Char Intro.
* WCOREDUMP: (libc)Process Completion Status.
* wcpcpy: (libc)Copying Strings and Arrays.
* wcpncpy: (libc)Truncating Strings.
* wcrtomb: (libc)Converting a Character.
* wcscasecmp: (libc)String/Array Comparison.
* wcscat: (libc)Concatenating Strings.
* wcschr: (libc)Search Functions.
* wcschrnul: (libc)Search Functions.
* wcscmp: (libc)String/Array Comparison.
* wcscoll: (libc)Collation Functions.
* wcscpy: (libc)Copying Strings and Arrays.
* wcscspn: (libc)Search Functions.
* wcsdup: (libc)Copying Strings and Arrays.
* wcsftime: (libc)Formatting Calendar Time.
* wcslen: (libc)String Length.
* wcsncasecmp: (libc)String/Array Comparison.
* wcsncat: (libc)Truncating Strings.
* wcsncmp: (libc)String/Array Comparison.
* wcsncpy: (libc)Truncating Strings.
* 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.
* wcstold: (libc)Parsing of Floats.
* wcstol: (libc)Parsing of Integers.
* 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.
* 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.
* wmemchr: (libc)Search Functions.
* wmemcmp: (libc)String/Array Comparison.
* wmemcpy: (libc)Copying Strings and Arrays.
* wmemmove: (libc)Copying Strings and Arrays.
* wmempcpy: (libc)Copying Strings and Arrays.
* wmemset: (libc)Copying Strings and Arrays.
* W_OK: (libc)Testing File Access.
* 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.
* WSTOPSIG: (libc)Process Completion Status.
* WTERMSIG: (libc)Process Completion Status.
* X_OK: (libc)Testing File Access.
* y0f: (libc)Special Functions.
* y0: (libc)Special Functions.
* y0l: (libc)Special Functions.
* y1f: (libc)Special Functions.
* y1: (libc)Special Functions.
* y1l: (libc)Special Functions.
* ynf: (libc)Special Functions.
* yn: (libc)Special Functions.
* ynl: (libc)Special Functions.
END-INFO-DIR-ENTRY


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.  For random numbers in cryptography, *note
Unpredictable Bytes::.

   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 C 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 C
     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)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     This function returns the next pseudo-random number in the
     sequence.  The value returned ranges from ‘0’ to ‘2147483647’.

     *NB:* 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)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     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: char * initstate (unsigned int SEED, char *STATE, size_t
          SIZE)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     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: char * setstate (char *STATE)
     Preliminary: | MT-Safe | AS-Unsafe lock | AC-Unsafe lock | *Note
     POSIX Safety Concepts::.

     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.  Besides this there is 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)
     Preliminary: | MT-Safe race:buf | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buf | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buf | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buf | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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])
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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])
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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])
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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])
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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 SEED16V
     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])
     Preliminary: | MT-Unsafe race:drand48 | AS-Unsafe | AC-Unsafe
     corrupt | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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, long int
          *RESULT)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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, long int
          *RESULT)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe race:buffer | AS-Safe | AC-Unsafe corrupt |
     *Note POSIX Safety Concepts::.

     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 kinds 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.
* Printing of Floats::          Converting floating-point numbers to strings.
* 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.
Similiarly, there are macros such as ‘INTMAX_WIDTH’ for the width of
these types.  Those macros for integer type widths come from TS
18661-1:2014.

   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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     The 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 iscanonical (_float-type_ X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     In some floating-point formats, some values have canonical
     (preferred) and noncanonical encodings (for IEEE interchange binary
     formats, all encodings are canonical).  This macro returns a
     nonzero value if X has a canonical encoding.  It is from TS
     18661-1:2014.

     Note that some formats have multiple encodings of a value which are
     all equally canonical; ‘iscanonical’ returns a nonzero value for
     all such encodings.  Also, formats may have encodings that do not
     correspond to any valid value of the type.  In ISO C terms these
     are "trap representations"; in the GNU C Library, ‘iscanonical’
     returns zero for such encodings.

 -- Macro: int isfinite (_float-type_ X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro returns a nonzero value if X is NaN. It is equivalent to

          (fpclassify (x) == FP_NAN)

 -- Macro: int issignaling (_float-type_ X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro returns a nonzero value if X is a signaling NaN (sNaN).
     It is from TS 18661-1:2014.

 -- Macro: int issubnormal (_float-type_ X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro returns a nonzero value if X is subnormal.  It is from
     TS 18661-1:2014.

 -- Macro: int iszero (_float-type_ X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro returns a nonzero value if X is zero.  It is from TS
     18661-1:2014.

   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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This function returns a nonzero value if X is a “not a number”
     value, and zero otherwise.

     *NB:* 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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.  When this interface is used, exceptions may not be
raised.

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 than 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’.)

 -- Macro: float SNANF
 -- Macro: double SNAN
 -- Macro: long double SNANL
     These macros, defined by TS 18661-1:2014, are constant expressions
     for signaling NaNs.

 -- Macro: int FE_SNANS_ALWAYS_SIGNAL
     This macro, defined by TS 18661-1:2014, is defined to ‘1’ in
     ‘fenv.h’ to indicate that functions and operations with signaling
     NaN inputs and floating-point results always raise the invalid
     exception and return a quiet NaN, even in cases (such as ‘fmax’,
     ‘hypot’ and ‘pow’) where a quiet NaN input can produce a non-NaN
     result.  Because some compiler optimizations may not handle
     signaling NaNs correctly, this macro is only defined if compiler
     support for signaling NaNs is enabled.  That support can be enabled
     with the GCC option ‘-fsignaling-nans’.

   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.


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)
     Preliminary: | MT-Safe | AS-Safe !posix | AC-Safe !posix | *Note
     POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 fesetexcept (int EXCEPTS)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This function sets the supported exception flags indicated by
     EXCEPTS, like ‘feraiseexcept’, but without causing enabled traps to
     be taken.  ‘fesetexcept’ is from TS 18661-1:2014.

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

 -- Function: int fetestexcept (int EXCEPTS)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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.

 -- Function: int fetestexceptflag (const fexcept_t *FLAGP, int EXCEPTS)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     Test whether the exception flags indicated by the parameter EXCEPTS
     are set in the variable pointed to by FLAGP.  If any of them are, a
     nonzero value is returned which specifies which exceptions are set.
     Otherwise the result is zero.  ‘fetestexceptflag’ is from TS
     18661-1:2014.


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 without loss of accuracy.  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, in the default rounding mode, return oo or -oo
as appropriate (in other rounding modes, the largest finite value of the
appropriate sign is returned when appropriate for that rounding mode).
They also set ERRNO to ‘ERANGE’ if returning oo or -oo; ERRNO may or may
not be set to ‘ERANGE’ when a finite value is returned on overflow.
When underflow occurs, the underflow exception is raised, and zero
(appropriately signed) or a subnormal value, as appropriate for the
mathematical result of the function and the rounding mode, is returned.
ERRNO may be set to ‘ERANGE’, but this is not guaranteed; it is intended
that the GNU C Library should set it when the underflow is to an
appropriately signed zero, but not necessarily for other underflows.

   When a math function has an argument that is a signaling NaN, the GNU
C Library does not consider this a domain error, so ‘errno’ is
unchanged, but the invalid exception is still raised (except for a few
functions that are specified to handle signaling NaNs differently).

   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.

   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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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, or 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::.

   *NB:* 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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.

TS 18661-1:2014 defines additional functions to save and restore
floating-point control modes (such as the rounding mode and whether
traps are enabled) while leaving other status (such as raised flags)
unchanged.

   The special macro ‘FE_DFL_MODE’ may be passed to ‘fesetmode’.  It
represents the floating-point control modes at program start.

 -- Function: int fegetmode (femode_t *MODEP)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     Store the floating-point control modes in the variable pointed to
     by MODEP.

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

 -- Function: int fesetmode (const femode_t *MODEP)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     Set the floating-point control modes to those described by MODEP.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This function enables traps for each of the exceptions as indicated
     by the parameter EXCEPTS.  The individual exceptions 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This function disables traps for each of the exceptions as
     indicated by the parameter EXCEPTS.  The individual exceptions 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 (void)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 its magnitude 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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, double EXPONENT)
 -- Function: float scalbf (float VALUE, float EXPONENT)
 -- Function: long double scalbl (long double VALUE, long double
          EXPONENT)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     The ‘scalb’ function is the BSD name for ‘ldexp’.

 -- Function: double scalbn (double X, int N)
 -- Function: float scalbnf (float X, int N)
 -- Function: long double scalbnl (long double X, int N)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     ‘scalbn’ is identical to ‘scalb’, except that the exponent N is an
     ‘int’ instead of a floating-point number.

 -- Function: double scalbln (double X, long int N)
 -- Function: float scalblnf (float X, long int N)
 -- Function: long double scalblnl (long double X, long int N)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     ‘scalbln’ is identical to ‘scalb’, except that the exponent N is a
     ‘long int’ instead of a floating-point number.

 -- Function: double significand (double X)
 -- Function: float significandf (float X)
 -- Function: long double significandl (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     ‘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.

   The ‘fromfp’ functions use the following macros, from TS
18661-1:2014, to specify the direction of rounding.  These correspond to
the rounding directions defined in IEEE 754-2008.

‘FP_INT_UPWARD’
     Round toward +oo.

‘FP_INT_DOWNWARD’
     Round toward -oo.

‘FP_INT_TOWARDZERO’
     Round toward zero.

‘FP_INT_TONEARESTFROMZERO’
     Round to nearest, ties round away from zero.

‘FP_INT_TONEAREST’
     Round to nearest, ties round to even.

 -- Function: double ceil (double X)
 -- Function: float ceilf (float X)
 -- Function: long double ceill (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions are similar to ‘rint’, but they round halfway cases
     away from zero instead of to the nearest integer (or other current
     rounding mode).

 -- Function: double roundeven (double X)
 -- Function: float roundevenf (float X)
 -- Function: long double roundevenl (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, from TS 18661-1:2014, are similar to ‘round’, but
     they round halfway cases to even instead of away from zero.

 -- Function: long int lrint (double X)
 -- Function: long int lrintf (float X)
 -- Function: long int lrintl (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions are just like ‘round’, but they return a ‘long long
     int’ instead of a floating-point number.

 -- Function: intmax_t fromfp (double X, int ROUND, unsigned int WIDTH)
 -- Function: intmax_t fromfpf (float X, int ROUND, unsigned int WIDTH)
 -- Function: intmax_t fromfpl (long double X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfp (double X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfpf (float X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfpl (long double X, int ROUND, unsigned int
          WIDTH)
 -- Function: intmax_t fromfpx (double X, int ROUND, unsigned int WIDTH)
 -- Function: intmax_t fromfpxf (float X, int ROUND, unsigned int WIDTH)
 -- Function: intmax_t fromfpxl (long double X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfpx (double X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfpxf (float X, int ROUND, unsigned int
          WIDTH)
 -- Function: uintmax_t ufromfpxl (long double X, int ROUND, unsigned
          int WIDTH)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, from TS 18661-1:2014, convert a floating-point
     number to an integer according to the rounding direction ROUND (one
     of the ‘FP_INT_*’ macros).  If the integer is outside the range of
     a signed or unsigned (depending on the return type of the function)
     type of width WIDTH bits (or outside the range of the return type,
     if WIDTH is larger), or if X is infinite or NaN, or if WIDTH is
     zero, a domain error occurs and an unspecified value is returned.
     The functions with an ‘x’ in their names raise the inexact
     exception when a domain error does not occur and the argument is
     not an integer; the other functions do not raise the inexact
     exception.

 -- 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions are like ‘fmod’ except that they round 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     ‘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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions are identical to the corresponding versions of
     ‘nextafter’ except that their second argument is a ‘long double’.

 -- Function: double nextup (double X)
 -- Function: float nextupf (float X)
 -- Function: long double nextupl (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     The ‘nextup’ function returns the next representable neighbor of X
     in the direction of positive infinity.  If X is the smallest
     negative subnormal number in the type of X the function returns
     ‘-0’.  If X = ‘0’ the function returns the smallest positive
     subnormal number in the type of X.  If X is NaN, NaN is returned.
     If X is +oo, +oo is returned.  ‘nextup’ is from TS 18661-1:2014.
     ‘nextup’ never raises an exception except for signaling NaNs.

 -- Function: double nextdown (double X)
 -- Function: float nextdownf (float X)
 -- Function: long double nextdownl (long double X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     The ‘nextdown’ function returns the next representable neighbor of
     X in the direction of negative infinity.  If X is the smallest
     positive subnormal number in the type of X the function returns
     ‘+0’.  If X = ‘0’ the function returns the smallest negative
     subnormal number in the type of X.  If X is NaN, NaN is returned.
     If X is -oo, -oo is returned.  ‘nextdown’ is from TS 18661-1:2014.
     ‘nextdown’ never raises an exception except for signaling NaNs.

 -- Function: double nan (const char *TAGP)
 -- Function: float nanf (const char *TAGP)
 -- Function: long double nanl (const char *TAGP)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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.

 -- Function: int canonicalize (double *CX, const double *X)
 -- Function: int canonicalizef (float *CX, const float *X)
 -- Function: int canonicalizel (long double *CX, const long double *X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     In some floating-point formats, some values have canonical
     (preferred) and noncanonical encodings (for IEEE interchange binary
     formats, all encodings are canonical).  These functions, defined by
     TS 18661-1:2014, attempt to produce a canonical version of the
     floating-point value pointed to by X; if that value is a signaling
     NaN, they raise the invalid exception and produce a quiet NaN. If a
     canonical value is produced, it is stored in the object pointed to
     by CX, and these functions return zero.  Otherwise (if a canonical
     value could not be produced because the object pointed to by X is
     not a valid representation of any floating-point value), the object
     pointed to by CX is unchanged and a nonzero value is returned.

     Note that some formats have multiple encodings of a value which are
     all equally canonical; when such an encoding is used as an input to
     this function, any such encoding of the same value (or of the
     corresponding quiet NaN, if that value is a signaling NaN) may be
     produced as output.

 -- Function: double getpayload (const double *X)
 -- Function: float getpayloadf (const float *X)
 -- Function: long double getpayloadl (const long double *X)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     IEEE 754 defines the "payload" of a NaN to be an integer value
     encoded in the representation of the NaN. Payloads are typically
     propagated from NaN inputs to the result of a floating-point
     operation.  These functions, defined by TS 18661-1:2014, return the
     payload of the NaN pointed to by X (returned as a positive integer,
     or positive zero, represented as a floating-point number); if X is
     not a NaN, they return an unspecified value.  They raise no
     floating-point exceptions even for signaling NaNs.

 -- Function: int setpayload (double *X, double PAYLOAD)
 -- Function: int setpayloadf (float *X, float PAYLOAD)
 -- Function: int setpayloadl (long double *X, long double PAYLOAD)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, defined by TS 18661-1:2014, set the object pointed
     to by X to a quiet NaN with payload PAYLOAD and a zero sign bit and
     return zero.  If PAYLOAD is not a positive-signed integer that is a
     valid payload for a quiet NaN of the given type, the object pointed
     to by X is set to positive zero and a nonzero value is returned.
     They raise no floating-point exceptions.

 -- Function: int setpayloadsig (double *X, double PAYLOAD)
 -- Function: int setpayloadsigf (float *X, float PAYLOAD)
 -- Function: int setpayloadsigl (long double *X, long double PAYLOAD)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, defined by TS 18661-1:2014, set the object pointed
     to by X to a signaling NaN with payload PAYLOAD and a zero sign bit
     and return zero.  If PAYLOAD is not a positive-signed integer that
     is a valid payload for a signaling NaN of the given type, the
     object pointed to by X is set to positive zero and a nonzero value
     is returned.  They raise no floating-point exceptions.


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.  TS 18661-1:2014 adds
such a macro for an equality comparison that _does_ raise an exception
for a NaN argument; it also adds functions that provide a total ordering
on all floating-point values, including NaNs, without raising any
exceptions even for signaling NaNs.

 -- Macro: int isgreater (_real-floating_ X, _real-floating_ Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro determines whether its arguments are unordered.  In
     other words, it is true if X or Y are NaN, and false otherwise.

 -- Macro: int iseqsig (_real-floating_ X, _real-floating_ Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     This macro determines whether its arguments are equal.  It is
     equivalent to ‘(X) == (Y)’, but it raises the invalid exception and
     sets ‘errno’ to ‘EDOM’ if either argument is a NaN.

 -- Function: int totalorder (double X, double Y)
 -- Function: int totalorderf (float X, float Y)
 -- Function: int totalorderl (long double X, long double Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions determine whether the total order relationship,
     defined in IEEE 754-2008, is true for X and Y, returning nonzero if
     it is true and zero if it is false.  No exceptions are raised even
     for signaling NaNs.  The relationship is true if they are the same
     floating-point value (including sign for zero and NaNs, and payload
     for NaNs), or if X comes before Y in the following order: negative
     quiet NaNs, in order of decreasing payload; negative signaling
     NaNs, in order of decreasing payload; negative infinity; finite
     numbers, in ascending order, with negative zero before positive
     zero; positive infinity; positive signaling NaNs, in order of
     increasing payload; positive quiet NaNs, in order of increasing
     payload.

 -- Function: int totalordermag (double X, double Y)
 -- Function: int totalordermagf (float X, float Y)
 -- Function: int totalordermagl (long double X, long double Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions determine whether the total order relationship,
     defined in IEEE 754-2008, is true for the absolute values of X and
     Y, returning nonzero if it is true and zero if it is false.  No
     exceptions are raised even for signaling NaNs.

   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.

   *NB:* 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 fminmag (double X, double Y)
 -- Function: float fminmagf (float X, float Y)
 -- Function: long double fminmagl (long double X, long double Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, from TS 18661-1:2014, return whichever of the two
     values X and Y has the smaller absolute value.  If both have the
     same absolute value, or either is NaN, they behave the same as the
     ‘fmin’ functions.

 -- Function: double fmaxmag (double X, double Y)
 -- Function: float fmaxmagf (float X, float Y)
 -- Function: long double fmaxmagl (long double X, long double Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions, from TS 18661-1:2014, return whichever of the two
     values X and Y has the greater absolute value.  If both have the
     same absolute value, or either is NaN, they behave the same as the
     ‘fmax’ functions.

 -- Function: double fdim (double X, double Y)
 -- Function: float fdimf (float X, float Y)
 -- Function: long double fdiml (long double X, long double Y)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 -pi to pi.

     ‘carg’ has a branch cut along the negative 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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     These functions return the projection of the complex value Z onto
     the Riemann sphere.  Values with an 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: Printing of Floats,  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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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
     ‘LLONG_MAX’ or ‘LLONG_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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     ‘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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     ‘strtouq’ is the BSD name for ‘strtoull’.

 -- Function: unsigned long long int wcstouq (const wchar_t *restrict
          STRING, wchar_t **restrict TAILPTR, int BASE)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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)
     Preliminary: | MT-Safe locale | AS-Safe | AC-Safe | *Note POSIX
     Safety Concepts::.

     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.

   See also *note Parsing of Integers::.


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

20.12 Printing of Floats
========================

The ‘strfrom’ functions are declared in ‘stdlib.h’.

 -- Function: int strfromd (char *restrict STRING, size_t SIZE, const
          char *restrict FORMAT, double VALUE)
 -- Function: int strfromf (char *restrict STRING, size_t SIZE, const
          char *restrict FORMAT, float VALUE)
 -- Function: int strfroml (char *restrict STRING, size_t SIZE, const
          char *restrict FORMAT, long double VALUE)
     Preliminary: | MT-Safe locale | AS-Unsafe heap | AC-Unsafe mem |
     *Note POSIX Safety Concepts::.

     The functions ‘strfromd’ (“string-from-double”), ‘strfromf’
     (“string-from-float”), and ‘strfroml’ (“string-from-long-double”)
     convert the floating-point number VALUE to a string of characters
     and stores them into the area pointed to by STRING.  The conversion
     writes at most SIZE characters and respects the format specified by
     FORMAT.

     The format string must start with the character ‘%’.  An optional
     precision follows, which starts with a period, ‘.’, and may be
     followed by a decimal integer, representing the precision.  If a
     decimal integer is not specified after the period, the precision is
     taken to be zero.  The character ‘*’ is not allowed.  Finally, the
     format string ends with one of the following conversion specifiers:
     ‘a’, ‘A’, ‘e’, ‘E’, ‘f’, ‘F’, ‘g’ or ‘G’ (*note Table of Output
     Conversions::).  Invalid format strings result in undefined
     behavior.

     These functions return the number of characters that would have
     been written to STRING had SIZE been sufficiently large, not
     counting the terminating null character.  Thus, the null-terminated
     output has been completely written if and only if the returned
     value is less than SIZE.

     These functions were introduced by ISO/IEC TS 18661-1.


File: libc.info,  Node: System V Number Conversion,  Prev: Printing of Floats,  Up: Arithmetic

20.13 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 the GNU C Library 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)
     Preliminary: | MT-Unsafe race:ecvt | AS-Unsafe | AC-Safe | *Note
     POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:fcvt | AS-Unsafe heap | AC-Unsafe mem
     | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     ‘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)
     Preliminary: | MT-Unsafe race:qecvt | AS-Unsafe | AC-Safe | *Note
     POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Unsafe race:qfcvt | AS-Unsafe heap | AC-Unsafe
     mem | *Note POSIX Safety Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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)
     Preliminary: | MT-Safe | AS-Safe | AC-Safe | *Note POSIX Safety
     Concepts::.

     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 C Library, 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:

     ‘time_t 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:

     ‘time_t 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 (struct timeval *result, struct timeval *x, struct timeval *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 GNU systems, 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 examining the process’ CPU time before
and after the computation.

   On GNU/Linux and GNU/Hurd systems, ‘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, see *note Resource Usage And Limitation::.

* Menu:

* CPU Time::                    The ‘clock’ function.
* Processor Time::              The ‘times’ function.