Hi Andries, Since you are the mathematician, can you comment? Thanks, Michael On Fri, Nov 26, 2010 at 9:57 AM, Richard B. Kreckel <kreckel@xxxxxxxx> wrote: > Hi! > > The man pages for cacos, cacosf, cacosl, catan, catanf, catanl, cacosh, > cacoshf, cacoshl, catanh, catanhf, and catanhl contain wrong maths. > > 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. > > I suspect that some of these errors are due to somebody trying to "simplify" > these formulae. Since this can ruin the behavior, I recommend to add a > comment to the upstream sources that warns against attempt of > simplification. > > For the sake of reference, I am looking at manpages-dev 3.25-1 on > Debian/squeeze. > > Bye! > -richy. > -- > Richard B. Kreckel > <http://www.ginac.de/~kreckel/> > -- Michael Kerrisk Linux man-pages maintainer; http://www.kernel.org/doc/man-pages/ Author of "The Linux Programming Interface"; http://man7.org/tlpi/ -- To unsubscribe from this list: send the line "unsubscribe linux-man" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
