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Michael Kerrisk 4c3fa19d23 cacos.3, cacosh.3, catan.3, catanh.3: Fix formula describing function 
The man pages for cacos(), cacosh(), catan(), catanh()
contain incorrect formulae describing the functions.

As reported by Richard B. Kreckel:

cacos, cacosf, cacosl:
    The formula given in the man page
      cacos(z) = -i clog(z + csqrt(z * z - 1))
    gives wrong results in second and fourth quadrant of
    complex plain.
    The formula
      cacos(z) = -i clog(z + I*csqrt(1 - z * z))
    gives correct results.

catan, catanf, catanl:
    The formula given in the man page
      catan(z) = 1 / 2i clog((1 + iz) / (1 - iz))
    gives wrong results on the negative imaginary axis beginning
    at -I (along one of the two branch cuts). Besides, the formula
    is written in an ambiguous way.
    The formula
      catan(z) = (clog(1 + iz) - clog(1 - iz)) / 2i
    gives correct results.

cacosh, cacoshf, cacoshl:
    The formula given in the man page
      cacosh(z) = (0.5) * clog((1 + z) / (1 - z))
    gives wrong results everywhere in the complex plain.
    (The formula seems to be copied from the one for catanh,
    where it is sometimes correct.)
    The formula
      cacosh(z) = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2))
    gives correct results.

catanh, catanhf, catanhl:
    The formula given in the man page
      catanh(z) = 0.5 * clog((1 + z) / (1 - z))
    gives wrong results on the positive real axis beginning at 1
    (along one of the two branch cuts).
    The formula
      catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))
    gives correct results.

I've also checked casin, casinf, casinl, casinh, casinhf, and
casinhl and the formulae given there
      casin(z) = -i clog(iz + csqrt(1 - z * z))
      casinh(z) = clog(z + csqrt(z * z + 1))
are actually correct.

Reported-by: Richard B. Kreckel <kreckel@ginac.de>
Reviewed-by: Andries Brouwer <Andries.Brouwer@cwi.nl>
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
 		2011-09-16 07:00:49 +02:00
man1 intro.1, time.1, accept.2, bind.2, connect.2, execve.2, flock.2, getdents.2, getpriority.2, getuid.2, intro.2, ioctl.2, mincore.2, mknod.2, personality.2, ptrace.2, read.2, recv.2, select_tut.2, send.2, sendfile.2, shmctl.2, sigaction.2, signal.2, stat.2, times.2, truncate.2, umask.2, wait.2, MB_CUR_MAX.3, MB_LEN_MAX.3, argz_add.3, btowc.3, clearenv.3, clock.3, cmsg.3, end.3, endian.3, errno.3, exit.3, fgetwc.3, fgetws.3, fopen.3, fputwc.3, fputws.3, fseek.3, fwide.3, getfsent.3, getgrnam.3, gethostid.3, getipnodebyname.3, getmntent.3, getpwnam.3, getwchar.3, grantpt.3, iconv.3, iconv_close.3, iconv_open.3, insque.3, intro.3, iswalnum.3, iswalpha.3, iswblank.3, iswcntrl.3, iswctype.3, iswdigit.3, iswgraph.3, iswlower.3, iswprint.3, iswpunct.3, iswspace.3, iswupper.3, iswxdigit.3, malloc.3, mblen.3, mbrlen.3, mbrtowc.3, mbsinit.3, mbsnrtowcs.3, mbsrtowcs.3, mbstowcs.3, mbtowc.3, mkstemp.3, mktemp.3, nl_langinfo.3, openpty.3, posix_openpt.3, printf.3, ptsname.3, putwchar.3, qecvt.3, rcmd.3, readdir.3, rexec.3, rpc.3, setnetgrent.3, shm_open.3, sigpause.3, stdin.3, stpcpy.3, strftime.3, strptime.3, syslog.3, towctrans.3, towlower.3, towupper.3, ttyslot.3, ungetwc.3, unlocked_stdio.3, wcpcpy.3, wcpncpy.3, wcrtomb.3, wcscasecmp.3, wcscat.3, wcschr.3, wcscmp.3, wcscpy.3, wcscspn.3, wcsdup.3, wcslen.3, wcsncasecmp.3, wcsncat.3, wcsncmp.3, wcsncpy.3, wcsnlen.3, wcsnrtombs.3, wcspbrk.3, wcsrchr.3, wcsrtombs.3, wcsspn.3, wcsstr.3, wcstok.3, wcstombs.3, wcswidth.3, wctob.3, wctomb.3, wctrans.3, wctype.3, wcwidth.3, wmemchr.3, wmemcmp.3, wmemcpy.3, wmemmove.3, wmemset.3, wprintf.3, console_ioctl.4, pts.4, elf.5, filesystems.5, hosts.5, proc.5, ttytype.5, boot.7, capabilities.7, credentials.7, epoll.7, glob.7, koi8-r.7, path_resolution.7, pty.7, signal.7, suffixes.7, time.7, unicode.7, unix.7, uri.7, utf-8.7: global fix: s/Unix/UNIX/ 2010-10-12 06:49:17 +02:00
man2 unlink.2: Improve EBUSY description 2011-09-16 07:00:48 +02:00
man3 cacos.3, cacosh.3, catan.3, catanh.3: Fix formula describing function 2011-09-16 07:00:49 +02:00
man4 console_codes.4: Add ESC [ 3 J 2011-09-16 07:00:48 +02:00
man5 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 2011-09-16 07:00:48 +02:00
man6 Wrapped long source lines 2008-07-06 15:10:32 +00:00
man7 unix.7: Add pointer to cmsg(3) for an example of use of SCM_RIGHTS 2011-09-16 07:00:48 +02:00
man8 add_key.2, keyctl.2, request_key.2, stime.2, time.2, ctime.3, difftime.3, ftime.3, getspnam.3, mq_receive.3, mq_send.3, rtime.3, sem_wait.3, string.3, timeradd.3, tzset.3, rtc.4, core.5, icmp.7, time.7, zic.8: Updated .TH timestamp 2010-02-25 10:43:57 +01:00
scripts find_repeated_words.sh: Fix bug 2010-08-29 14:41:52 +02:00
Changes Start of man-pages-3.33: updating Changes and Changes.old 2010-12-03 08:07:15 +01:00
Changes.old Changes.old: spfix 2011-09-16 07:00:45 +02:00
Makefile POSIX man pages are now in a separate package. 2008-06-05 09:52:50 +00:00
README README: Point directly at contributing.html 2010-08-29 07:40:29 +02:00
man-pages-3.33.Announce Start of man-pages-3.33: updating .Announce and .lsm files 2010-12-03 08:07:15 +01:00
man-pages-3.33.lsm Start of man-pages-3.33: updating .Announce and .lsm files 2010-12-03 08:07:15 +01:00

README 

This package contains Linux man pages for sections
2, 3, 4, 5, and 7. Some more information is given in the
`Announce' file.

Install by copying to your favourite location.
"make install" will just copy them to /usr/share/man/man[1-8].
"make" will move the pages from this package that are older than
the already installed ones to a subdirectory `not_installed',
then remove old versions (compressed or not),
compress the pages, and copy them to /usr/share/man/man[1-8].


Note that you may have to remove preformatted pages.

Note that sometimes these pages are duplicates of pages
also distributed in other packages. This has been reported
about dlclose.3, dlerror.3, dlopen.3, dlsym.3 (found in ld.so),
about resolver.3, resolv.conf.5 (found in bind-utils),
and about passwd.5, and mailaddr.7. Be careful not to
overwrite more up-to-date versions.
Reports on further duplicates are welcome.
Formerly present and now removed duplicates:
 exports.5 (found in nfs-server-2.2*),
 fstab.5, nfs.5 (found in util-linux-2.12*),
 lilo.8, lilo.conf.5 (found in lilo-21.6*).

Copyrights: These man pages come under various copyrights.
All pages are freely distributable when the nroff source is included.

If you have corrections and additions to suggest, see
http://www.kernel.org/doc/man-pages/contributing.html