1.\" Copyright (c) 2007-2008 David Schultz <das@FreeBSD.org> 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.\" $FreeBSD$ 26.\" 27.Dd November 4, 2018 28.Dt CSQRT 3 29.Os 30.Sh NAME 31.Nm csqrt , 32.Nm csqrtf , 33.Nm csqrtl 34.Nd complex square root functions 35.Sh LIBRARY 36.Lb libm 37.Sh SYNOPSIS 38.In complex.h 39.Ft double complex 40.Fn csqrt "double complex z" 41.Ft float complex 42.Fn csqrtf "float complex z" 43.Ft long double complex 44.Fn csqrtl "long double complex z" 45.Sh DESCRIPTION 46The 47.Fn csqrt , 48.Fn csqrtf , 49and 50.Fn csqrtl 51functions compute the square root of 52.Fa z 53in the complex plane, with a branch cut along the negative real axis. 54In other words, 55.Fn csqrt , 56.Fn csqrtf , 57and 58.Fn csqrtl 59always return the square root whose real part is non-negative. 60.Sh RETURN VALUES 61These functions return the requested square root. 62The square root of 0 is 63.Li +0 \*(Pm 0 , 64where the imaginary parts of the input and respective result have 65the same sign. 66For infinities and \*(Nas, the following rules apply, with the 67earlier rules having precedence: 68.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)" 69.Em "Input" Ta Em "Result" Ta \& 70k + \*(If*I \*(If + \*(If*I (for all k) 71-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I \& 72\*(If + \*(Na*I \*(If + \*(Na*I \& 73k + \*(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 \& 77.El 78.Pp 79For numbers with negative imaginary parts, the above special cases 80apply given the identity: 81.Dl csqrt(conj(z)) = conj(csqrt(z)) 82Note that the sign of \*(Na is indeterminate. 83Also, if the real or imaginary part of the input is finite and 84an \*(Na is generated, an invalid exception will be thrown. 85.Sh SEE ALSO 86.Xr cabs 3 , 87.Xr fenv 3 , 88.Xr math 3 89.Sh STANDARDS 90The 91.Fn csqrt , 92.Fn csqrtf , 93and 94.Fn csqrtl 95functions conform to 96.St -isoC-99 . 97.Sh BUGS 98For 99.Fn csqrt 100and 101.Fn csqrtl , 102inexact results are not always correctly rounded. 103