2004-11-03 13:51:07 +00:00
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.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\" Distributed under GPL
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.\" Based on glibc infopages
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2008-08-01 05:26:49 +00:00
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.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
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.\" <mtk.manpages@gmail.com>
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2004-11-15 08:24:41 +00:00
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.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
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.\" <kreutz@dbs.uni-hannover.de>
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_exit.2, brk.2, capget.2, chdir.2, chmod.2, chown.2, chroot.2, getdtablesize.2, gethostname.2, getpagesize.2, getsid.2, killpg.2, mknod.2, mknodat.2, poll.2, posix_fadvise.2, pread.2, readlink.2, setpgid.2, setreuid.2, sigaltstack.2, stat.2, symlink.2, sync.2, truncate.2, vfork.2, wait.2, wait4.2, a64l.3, abs.3, acos.3, acosh.3, asin.3, asinh.3, atan.3, atan2.3, atoi.3, cbrt.3, ceil.3, copysign.3, cosh.3, dirfd.3, div.3, ecvt.3, erf.3, erfc.3, exp.3, exp2.3, fabs.3, fdim.3, ffs.3, floor.3, fma.3, fmax.3, fmin.3, fmod.3, fpclassify.3, frexp.3, ftw.3, fwide.3, gcvt.3, getcwd.3, getdate.3, getgrent.3, gethostid.3, getpass.3, getpwent.3, getsubopt.3, getw.3, hypot.3, ilogb.3, index.3, isalpha.3, isgreater.3, iswblank.3, j0.3, ldexp.3, lockf.3, log.3, log10.3, log1p.3, logb.3, lrint.3, lround.3, mkstemp.3, mktemp.3, modf.3, mq_receive.3, mq_send.3, nan.3, nextafter.3, posix_fallocate.3, posix_memalign.3, printf.3, qecvt.3, random.3, realpath.3, remainder.3, remquo.3, rint.3, round.3, scalb.3, scalbln.3, scanf.3, siginterrupt.3, signbit.3, sigset.3, sinh.3, sqrt.3, strcasecmp.3, strcat.3, strchr.3, strcmp.3, strcoll.3, strcpy.3, strfry.3, strpbrk.3, strsep.3, strspn.3, strstr.3, strtod.3, strtok.3, strtol.3, strtoul.3, strxfrm.3, tanh.3, tgamma.3, trunc.3, ttyslot.3, ualarm.3, usleep.3, wprintf.3, armscii-8.7, cp1251.7, iso_8859-10.7, iso_8859-11.7, iso_8859-13.7, iso_8859-14.7, iso_8859-3.7, iso_8859-5.7, iso_8859-6.7, iso_8859-8.7, koi8-u.7: tstamp
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2010-09-19 17:19:13 +00:00
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.TH TGAMMA 3 2010-09-20 "GNU" "Linux Programmer's Manual"
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2004-11-03 13:51:07 +00:00
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.SH NAME
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tgamma, tgammaf, tgammal \- true gamma function
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.SH SYNOPSIS
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.B #include <math.h>
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.sp
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.BI "double tgamma(double " x );
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.br
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.BI "float tgammaf(float " x );
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.br
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.BI "long double tgammal(long double " x );
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.sp
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2007-07-08 12:11:40 +00:00
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Link with \fI\-lm\fP.
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.sp
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.in -4n
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Feature Test Macro Requirements for glibc (see
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.BR feature_test_macros (7)):
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.in
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.sp
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.ad l
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.BR tgamma (),
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.BR tgammaf (),
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.BR tgammal ():
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2010-09-18 15:46:06 +00:00
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.RS 4
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2010-09-18 15:46:42 +00:00
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_XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE ||
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_POSIX_C_SOURCE\ >=\ 200112L;
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2010-09-18 15:46:06 +00:00
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.br
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or
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2007-07-08 12:11:40 +00:00
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.I cc\ -std=c99
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2010-09-18 15:46:06 +00:00
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.RE
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.ad
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2004-11-03 13:51:07 +00:00
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.SH DESCRIPTION
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The Gamma function is defined by
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.sp
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2008-08-01 05:26:49 +00:00
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Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
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2004-11-03 13:51:07 +00:00
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.sp
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2010-01-16 16:47:13 +00:00
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It is defined for every real number except for nonpositive integers.
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_syscall.2, accept.2, epoll_create.2, inotify_add_watch.2, ioctl.2, msgget.2, msgop.2, open.2, prctl.2, sched_setscheduler.2, semctl.2, semget.2, swapon.2, addseverity.3, cacosh.3, csqrt.3, dirfd.3, drand48.3, fputws.3, mq_send.3, posix_openpt.3, puts.3, sched_getcpu.3, shm_open.3, sqrt.3, sysconf.3, tgamma.3, ulimit.3, credentials.7, svipc.7: Global fix: s/non-negative/nonnegative/
The tendency in English, as prescribed in style guides like
Chicago MoS, is towards removing hyphens after prefixes
like "non-" etc.
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2010-01-16 16:44:48 +00:00
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For nonnegative integral \fIm\fP one has
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2004-11-03 13:51:07 +00:00
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.sp
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2008-08-01 05:26:49 +00:00
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Gamma(m+1) = m!
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2004-11-03 13:51:07 +00:00
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.sp
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and, more generally, for all \fIx\fP:
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.sp
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2008-08-01 05:26:49 +00:00
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Gamma(x+1) = x * Gamma(x)
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2004-11-03 13:51:07 +00:00
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.sp
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2004-11-15 08:24:41 +00:00
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Furthermore, the following is valid for all values of \fIx\fP
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outside the poles:
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2004-11-03 13:51:07 +00:00
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.sp
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2008-08-01 05:26:49 +00:00
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Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
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2004-11-03 13:51:07 +00:00
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.PP
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2008-08-01 05:26:49 +00:00
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.SH RETURN VALUE
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On success, these functions return Gamma(x).
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If
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.I x
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is a NaN, a NaN is returned.
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If
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2007-07-09 20:43:38 +00:00
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.I x
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2008-08-01 05:26:49 +00:00
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is positive infinity, positive infinity is returned.
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If
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2007-07-09 20:43:38 +00:00
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.I x
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is a negative integer, or is negative infinity,
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2008-08-04 16:00:58 +00:00
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a domain error occurs,
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2008-08-01 05:26:49 +00:00
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and a NaN is returned.
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If the result overflows,
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2008-08-04 16:00:58 +00:00
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a range error occurs,
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2008-08-01 05:26:49 +00:00
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and the functions return
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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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respectively, with the correct mathematical sign.
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If the result underflows,
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2008-08-04 16:00:58 +00:00
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a range error occurs,
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2008-08-01 05:26:49 +00:00
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and the functions return 0, with the correct mathematical sign.
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If
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2007-07-09 20:43:38 +00:00
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.I x
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fallocate.2, kexec_load.2, poll.2, spu_run.2, atan2.3, cbrt.3, clock_getcpuclockid.3, end.3, frexp.3, getgrouplist.3, getifaddrs.3, matherr.3, modf.3, pow.3, pthread_getattr_np.3, pthread_getcpuclockid.3, sched_getcpu.3, tgamma.3, mouse.4, proc.5, feature_test_macros.7, spufs.7: Global fix: properly escape minus sign
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2011-09-10 01:57:53 +00:00
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is \-0 or +0,
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2008-08-04 16:00:58 +00:00
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a pole error occurs,
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2008-08-01 05:26:49 +00:00
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and the functions return
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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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respectively, with the same sign as the 0.
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.SH ERRORS
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See
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.BR math_error (7)
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for information on how to determine whether an error has occurred
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when calling these functions.
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.PP
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The following errors can occur:
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.TP
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2008-09-29 09:00:36 +00:00
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Domain error: \fIx\fP is a negative integer, or negative infinity
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2008-08-01 05:26:49 +00:00
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.\" FIXME . errno is not set to EDOM for x == -inf
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
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.I errno
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is set to
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.BR EDOM .
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An invalid floating-point exception
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.RB ( FE_INVALID )
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is raised (but see BUGS).
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.TP
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Pole error: \fIx\fP is +0 or \-0
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.I errno
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is set to
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.BR ERANGE .
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A divide-by-zero floating-point exception
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.RB ( FE_DIVBYZERO )
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is raised.
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.TP
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Range error: result overflow
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.I errno
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is set to
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.BR ERANGE .
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An overflow floating-point exception
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.RB ( FE_OVERFLOW )
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is raised.
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.PP
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glibc also gives the following error which is not specified
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2008-09-29 09:00:36 +00:00
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in C99 or POSIX.1-2001.
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2008-08-01 05:26:49 +00:00
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.TP
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Range error: result underflow
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.\" e.g., tgamma(-172.5) on glibc 2.8/x86-32
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.\" .I errno
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.\" is set to
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.\" .BR ERANGE .
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An underflow floating-point exception
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.RB ( FE_UNDERFLOW )
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is raised.
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.IP
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.I errno
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is not set for this case.
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.\" FIXME . Is it intentional that errno is not set:
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
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.\"
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.\" glibc (as at 2.8) also supports and an inexact
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.\" exception for various cases.
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2008-08-11 17:13:47 +00:00
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.SH VERSIONS
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These functions first appeared in glibc in version 2.1.
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2004-11-03 13:51:07 +00:00
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.SH "CONFORMING TO"
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2008-08-01 05:26:49 +00:00
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C99, POSIX.1-2001.
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.SH NOTES
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This function had to be called "true gamma function"
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since there is already a function
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.BR gamma (3)
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2008-08-01 05:54:27 +00:00
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that returns something else (see
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.BR gamma (3)
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for details).
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2008-08-01 05:26:49 +00:00
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.SH BUGS
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If
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.I x
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is negative infinity,
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.I errno
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is not set (it should be set to
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2008-08-06 06:12:44 +00:00
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.BR EDOM ).
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2008-08-01 05:26:49 +00:00
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
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2008-08-10 15:10:08 +00:00
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2008-08-10 15:11:07 +00:00
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In glibc versions 2.3.3 and earlier,
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fallocate.2, kexec_load.2, poll.2, spu_run.2, atan2.3, cbrt.3, clock_getcpuclockid.3, end.3, frexp.3, getgrouplist.3, getifaddrs.3, matherr.3, modf.3, pow.3, pthread_getattr_np.3, pthread_getcpuclockid.3, sched_getcpu.3, tgamma.3, mouse.4, proc.5, feature_test_macros.7, spufs.7: Global fix: properly escape minus sign
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2011-09-10 01:57:53 +00:00
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an argument of +0 or \-0 incorrectly produced a domain error
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2008-08-10 15:10:08 +00:00
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.RI ( errno
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set to
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.B EDOM
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and an
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.B FE_INVALID
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exception raised), rather than a pole error.
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2004-11-03 13:51:07 +00:00
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.SH "SEE ALSO"
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.BR gamma (3),
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.BR lgamma (3)
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