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Message-ID: <8e1c2d48-3c46-b7fa-da1c-11907337d69d@polimi.it>
Date: Thu, 17 May 2018 14:32:40 +0200
From: Paolo Mantegazza <paolo.mantegazza@...imi.it>
To: musl@...ts.openwall.com
Subject: What should be the result of CACOSH(F)(CCOSH(F)(-2 + 1j))?
Hi,
calling: j = sqrt(-1),
MUSL answer is: -0.200000e+1 + 0.100000e+1j;
GLIBC answer is: +0.20000e+1 - 0.100000e+1j;
SCILAB answer is: +0.20000e+1 - 0.100000e+1j;
MATLAB answer is: +0.20000e+1 - 0.100000e+1j;
UCLIB-NG answer is: +0.20000e+1 - 0.100000e+1j;
Math is not democracy so maybe MUSL's answer is the right one. In fact,
with infinite precision at least, one should expect that, by applying
the inverse of a function to a function, the result should be the used
function argument.
So, does it either show a missed correct principal value or that MUSL is
the smartest one?
In any case, following:
http://mathworld.wolfram.com/InverseHyperbolicCosine.html, a way to have
MUSL match GLIBC:SCILAB:MATLAB:UCLIB-NG is to change the two code lines
in MUSL ./src/complex/cacosh.c
z = cacos(z);
return CMPLX(-cimag(z), creal(z)); // AKA j*cacos(z)
into
return = clog(z + csqrt(z + 1) * csqrt(z - 1)); // AKA a
definition of cacosh
As a further info, NEWLIB cacosh.c (not tested here) recites:
#if 0 /* does not give the principal value */
w = I * cacos(z);
#else
w = clog(z + csqrt(z + 1) * csqrt(z - 1));
#endif
return w;
it should be remarked that, to provide the correct principal value using
just cacos(z), the above mentioned link addresses the need of testing
the cacosh argument in order to appropriately use either j*cacos(z) or
-j*cacos(z). It is therefore likely that the fix to be chosen, if any,
should be based on computational efficiency.
Once more math is not democracy, so the answer must be left to the math
savviest.
Regards, Paolo Mantegazza.
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