error in computing atanh

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Francisco Peñuñuri
编辑： Francisco Peñuñuri 2021-2-13
When computing atanh(3.1) in R2018.a and R2020.a the complex part has positive sign.
When computing in fortran (and Mathematica) the result is negative.

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David Goodmanson
David Goodmanson 2021-2-13
编辑：David Goodmanson 2021-2-13
Hello Francisco,
The imaginary part is i*pi/2, so the two answers are a+i*pi/2 and a-i*pi/2, where a is real. Both answers are equally valid, so unless an answer is violating some prearranged standard set by the particular software invoked, there is not an error. Note that
tanh(a+i*b) = tanh(a+i*b+i*n*pi)
so there is an ambiguity modulo i*pi in the atahh function..
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John D'Errico
John D'Errico 2021-2-13
But there is no international standards commission that decides which is the principal branch to take on some multi-valued result. And while it seems pretty standard to take the POSITIVE branch for a sqrt, so it may have seemed just as logical to take the positive branch here.
The result is valid and non-unique. You cannot say more than that.
Francisco Peñuñuri
Francisco Peñuñuri 2021-2-13
编辑：Francisco Peñuñuri 2021-2-13
I agree with you. Still, is somehow awkward that sqrt(4) gives the principal value (regardless if this is positive or negative) while atanh(3.1) does not. I will accept the answer.
Thank you very much.

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