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.Dd November 4, 2018 26.Dt CSQRT 3 27.Os 28.Sh NAME 29.Nm csqrt , 30.Nm csqrtf , 31.Nm csqrtl 32.Nd complex square root functions 33.Sh LIBRARY 34.Lb libm 35.Sh SYNOPSIS 36.In complex.h 37.Ft double complex 38.Fn csqrt "double complex z" 39.Ft float complex 40.Fn csqrtf "float complex z" 41.Ft long double complex 42.Fn csqrtl "long double complex z" 43.Sh DESCRIPTION 44The 45.Fn csqrt , 46.Fn csqrtf , 47and 48.Fn csqrtl 49functions compute the square root of 50.Fa z 51in the complex plane, with a branch cut along the negative real axis. 52In other words, 53.Fn csqrt , 54.Fn csqrtf , 55and 56.Fn csqrtl 57always return the square root whose real part is non-negative. 58.Sh RETURN VALUES 59These functions return the requested square root. 60The square root of 0 is 61.Li +0 \*(Pm 0 , 62where the imaginary parts of the input and respective result have 63the same sign. 64For infinities and \*(Nas, the following rules apply, with the 65earlier 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 \& 68k + \*(If*I \*(If + \*(If*I (for all k) 69-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I \& 70\*(If + \*(Na*I \*(If + \*(Na*I \& 71k + \*(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 \& 75.El 76.Pp 77For numbers with negative imaginary parts, the above special cases 78apply given the identity: 79.Dl csqrt(conj(z)) = conj(csqrt(z)) 80Note that the sign of \*(Na is indeterminate. 81Also, if the real or imaginary part of the input is finite and 82an \*(Na is generated, an invalid exception will be thrown. 83.Sh SEE ALSO 84.Xr cabs 3 , 85.Xr fenv 3 , 86.Xr math 3 87.Sh STANDARDS 88The 89.Fn csqrt , 90.Fn csqrtf , 91and 92.Fn csqrtl 93functions conform to 94.St -isoC-99 . 95.Sh BUGS 96For 97.Fn csqrt 98and 99.Fn csqrtl , 100inexact results are not always correctly rounded. 101