[6248] in s-news-athena
Bug / Inconsistency of cosh / cos, ... with complex numbers
daemon@ATHENA.MIT.EDU (Martin Maechler)
Tue Jan 24 13:57:49 1995
From: Martin Maechler <maechler@stat.math.ethz.ch>
Date: Tue, 24 Jan 1995 18:47:02 +0100
To: S-News <s-news@utstat.toronto.edu>
Cc: maechler@stat.math.ethz.ch
Reply-To: Martin Maechler <maechler@stat.math.ethz.ch>
[ This is Splus 3.2, on Sun SPARC, SunOS 4.1.3 ]
The real bug may well lie in
the IEEE arithmetic / dealing with 'Complex INFINITY'
Consider the following example:
z <- 100*5:10 + 0*1i ### These are real numbers 'disguised' as complex...
z ## is mathematically the same as Re(z) !
##>> [1] 500+0i 600+0i 700+0i 800+0i 900+0i 1000+0i
cosh(z) ## oops: see the jump ?
##>> [1] 7.018e+216+0i 1.8865e+260+0i 5.0712e+303+0i 8.000e+02+0i 9.000e+02+0i
##>> [6] 1.000e+03+0i
cosh(Re(z)) ## should be the same as above, but this time is correct
##>> [1] 7.0180e+216 1.8865e+260 5.0712e+303 Inf Inf Inf
Re(cosh(Re(z)))
##>> [1] 7.0180e+216 1.8865e+260 5.0712e+303 Inf Inf Inf
Re(cosh(z)) ## here you see the jump even better ...
##>> [1] 7.0180e+216 1.8865e+260 5.0712e+303 8.0000e+02 9.0000e+02 1.0000e+03
#### NOTE: sinh(z) gives identical answers (which at least is consistent..)
In conclusion, the hyperbolic (co)sine
(but this is also true for cos(), sin() with approp.arguments !!!)
becomes non-monotone for the positive reals,
even though it's well known to be a monotone function there....
--- an average user would consider this to be a bug ...
Martin Maechler <maechler@stat.math.ethz.ch> <>< _
Seminar fuer Statistik, SOL F5 _| |_
ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND |_ _|
phone: x-41-1-632-3408 fax: ...-1086 |_|
