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