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32 .Nd complex square root functions
38 .Fn csqrt "double complex z"
40 .Fn csqrtf "float complex z"
41 .Ft long double complex
42 .Fn csqrtl "long double complex z"
49 functions compute the square root of
51 in the complex plane, with a branch cut along the negative real axis.
57 always return the square root whose real part is non-negative.
59 These functions return the requested square root.
60 The square root of 0 is
62 where the imaginary parts of the input and respective result have
64 For infinities and \*(Nas, the following rules apply, with the
65 earlier rules having precedence:
66 .Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)"
67 .Em "Input" Ta Em "Result" Ta \&
68 k + \*(If*I \*(If + \*(If*I (for all k)
69 -\*(If + \*(Na*I \*(Na \*(Pm \*(If*I \&
70 \*(If + \*(Na*I \*(If + \*(Na*I \&
71 k + \*(Na*I \*(Na + \*(Na*I \&
72 \*(Na + k*I \*(Na + \*(Na*I \&
73 -\*(If + k*I +0 + \*(If*I \&
74 \*(If + k*I \*(If + 0*I \&
77 For numbers with negative imaginary parts, the above special cases
78 apply given the identity:
79 .Dl csqrt(conj(z)) = conj(csqrt(z))
80 Note that the sign of \*(Na is indeterminate.
81 Also, if the real or imaginary part of the input is finite and
82 an \*(Na is generated, an invalid exception will be thrown.
100 inexact results are not always correctly rounded.