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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