1.\" Copyright (c) 2007 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 December 14, 2007 28.Dt CSQRT 3 29.Os 30.Sh NAME 31.Nm csqrt , 32.Nm csqrtf 33.Nd complex square root functions 34.Sh LIBRARY 35.Lb libm 36.Sh SYNOPSIS 37.In complex.h 38.Ft double complex 39.Fn csqrt "double complex z" 40.Ft float complex 41.Fn csqrtf "float complex z" 42.Sh DESCRIPTION 43The 44.Fn csqrt 45and 46.Fn csqrtf 47functions compute the square root of 48.Fa z 49in the complex plane, with a branch cut along the negative real axis. 50In other words, 51.Fn csqrt 52and 53.Fn csqrtf 54always return the square root whose real part is non-negative. 55.Sh RETURN VALUES 56These functions return the requested square root. 57The square root of 0 is 58.Li +0 \*(Pm 0 , 59where the imaginary parts of the input and respective result have 60the same sign. 61For infinities and \*(Nas, the following rules apply, with the 62earlier rules having precedence: 63.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)" 64.Em Input Result 65k + \*(If*I \*(If + \*(If*I (for all k) 66-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I 67\*(If + \*(Na*I \*(If + \*(Na*I 68k + \*(Na*I \*(Na + \*(Na*I 69\*(Na + k*I \*(Na + \*(Na*I 70-\*(If + k*I +0 + \*(If*I 71\*(If + k*I \*(If + 0*I 72.El 73.Pp 74For numbers with negative imaginary parts, the above special cases 75apply given the identity: 76.Dl csqrt(conj(z) = conj(sqrt(z)) 77Note that the sign of \*(Na is indeterminate. 78Also, if the real or imaginary part of the input is finite and 79an \*(Na is generated, an invalid exception will be thrown. 80.Sh SEE ALSO 81.Xr cabs 3 , 82.Xr fenv 3 , 83.Xr math 3 , 84.Sh STANDARDS 85The 86.Fn csqrt 87and 88.Fn csqrtf 89functions conform to 90.St -isoC-99 . 91.Sh BUGS 92For 93.Fn csqrt , 94inexact results are not correctly rounded in general. 95